Can a refrigerator that is 21.5 cubic feet fit in a space that is 21 cubic feet?
No, a refrigerator that is 21.5 cubic feet cannot fit in a space that is only 21 cubic feet. The refrigerator would be too big for the space.
What is the volume of a cube with a side length of 1.5 in.?(1 point)
? in.3
The volume of a cube with a side length of 1.5 in. is (1.5 in)³ = 3.375 in³. Answer: 3.375 in³.
you promise? That doesn't make sense to me
Yes, I promise. To calculate the volume of a cube, you need to cube the length of its sides. In this case, the length of sides is 1.5 inches, so you need to cube 1.5.
(1.5 in)³ = 1.5 in x 1.5 in x 1.5 in = 3.375 in³.
So, the volume of the cube is 3.375 cubic inches.
If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2, what is the height of this prism?
? in.
The formula to find the volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height of the prism.
Given that the volume of the right rectangular prism is 1.5 in^3 and the product of length and width is 1.5 in^2, we can write:
lw = 1.5 in^2
And
lwh = 1.5 in^3
Substituting lw = 1.5 in^2 in the second equation, we get:
1.5h = 1.5
Dividing both sides by 1.5, we get:
h = 1
Therefore, the height of the prism is 1 inch. Answer: 1 in.
Lloyd bought a refrigerator that measures 76 cm×76 cm×170 cm to fit in a space with a volume of 975,000 cm3. Will the refrigerator fit in the space? Explain.
To find out if the refrigerator will fit in the space, we need to compute the volume of the refrigerator and compare it with the given space volume.
The volume of the refrigerator is given by the product of its length, width, and height:
Volume of the refrigerator = 76 cm x 76 cm x 170 cm = 949,600 cm³
The given space has a volume of 975,000 cm³.
Comparing these two volumes, we can see that the volume of the refrigerator is less than the space volume. So, the refrigerator will fit in the space with some room to spare.
Answer: Yes, the refrigerator will fit in the space.
Use the image to answer the question.
An illustration shows a rectangular pyramid with length of 7.5 miles, a width of 7 miles, and a perpendicular height of 5 miles. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
What is the volume of the rectangular pyramid?
? mi.3
The formula to find the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
In this case, the base is a rectangle with a length of 7.5 miles and a width of 7 miles, so its area is:
B = length x width = 7.5 miles x 7 miles = 52.5 square miles
The height of the pyramid is given as 5 miles.
Therefore, the volume of the pyramid is:
V = (1/3)Bh = (1/3)(52.5 square miles)(5 miles) = 87.5 cubic miles
So, the volume of the rectangular pyramid is 87.5 cubic miles.
Answer: 87.5 mi³.
A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?
? cm3
The formula to find the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
In this case, the base is a rectangle with a width of 4 cm and a length of 9 cm, so its area is:
B = width x length = 4 cm x 9 cm = 36 square cm
The height of the pyramid is given as 21 cm.
Therefore, the volume of the pyramid is:
V = (1/3)Bh = (1/3)(36 square cm)(21 cm) = 252 cubic cm
So, the volume of the slice of cheese is 252 cubic centimeters.
Answer: 252 cm³.
A rectangular prism has a volume of 27 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
? in.3
The volume of a rectangular pyramid with base area B and height h is given by the formula V = (1/3)Bh.
In this case, the base of the pyramid is congruent to the base of the rectangular prism, which means the area of the base of the pyramid is the same as the area of the base of the prism.
Since the volume of the prism is 27 in³, and the length, width, and height are equal, we can set up the equation:
V = lwh = s³ = 27 in³
where s is the length of each side.
Solving this equation, we get:
s = 3 in
So, the base of the pyramid has an area of:
B = lw = (3 in)(3 in) = 9 in²
The height of the pyramid is also equal to 3 in, since it's congruent to the height of the prism.
Therefore, the volume of the pyramid is:
V = (1/3)Bh = (1/3)(9 in²)(3 in) = 9 in³
So, the volume of the pyramid is 9 cubic inches.
Answer: 9 in³.
A rectangular pyramid has a volume of 480 in.3. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
? in.3
The volume of a rectangular pyramid with base area B and height h is given by the formula V = (1/3)Bh.
In this case, the volume of the pyramid is given as 480 in³. Therefore, we can write:
V = (1/3)Bh = 480 in³
The base of the pyramid is congruent to the base of the rectangular prism, which means the area of the base of the pyramid is the same as the area of the base of the prism. Let's denote the base length and width as l and w, respectively. Since the height of the pyramid and the prism is congruent, we have h = h.
So, the volume of the rectangular prism is given by:
V = lwh
Since the base of the pyramid is congruent to the base of the prism, we have:
B = lw
Therefore, we can rewrite the volume of the pyramid as:
V = (1/3)Bh = (1/3)(lw)h = (lwh)/3
Substituting lwh from the volume formula for the prism, we have:
(lwh)/3 = 480 in³
Multiplying both sides by 3:
lwh = 1440 in³
But we know that l = w (since the base of the prism is a square) and h = h. So,
lwh = l²h
Substituting we get:
l²h = 1440 in³
Now, we have two variables and only one equation. However, we know that the dimensions of a pyramid cannot be negative. This means that both l and h must have positive values. We also know that l = w, which means that l and w must be equal. Therefore, we can substitute l for w and rewrite the equation as:
l³ = 1440 in³
Taking the cube root of both sides:
l = 12 in
So, the base of the rectangular prism has dimensions 12 x 12 in, and the height (which is equal to the height of the pyramid) is h = 20 in.
Therefore, the volume of the rectangular prism is:
V = lwh = (12 in)(12 in)(20 in) = 2880 in³
So, the volume of the rectangular prism is 2880 cubic inches.
Answer: 2880 in³
An illustration shows a triangular pyramid and a triangular prism. The edges that are not visible are marked as dashed lines. The triangular pyramid has the triangular face as its base. The sides of of the triangular base measure 3 inches and 5 inches. The perpendicular height of the pyramid is 8.41 inches. The triangular prism has its triangular face as the base. The sides of the triangular base measure 3 inches and 5 inches. The length of the side is 8.41 inches.
Which shape has the larger volume? How much larger is it?
The pyramid has a larger volume by three times.
The volumes are the same.
The prism has a larger volume by 13 times.
The prism has a larger volume by three times.
The pyramid and the prism have congruent triangular bases with sides 3 inches, 5 inches, and a height of 8.41 inches.
The volume of the triangular pyramid is given by the formula V = (1/3)Bh, where B is the area of the triangular base and h is the height of the pyramid.
The area of the triangular base is given by the formula A = (1/2)bh, where b is the base of the triangle and h is the height of the triangle.
Substituting the values given, we get:
B = (1/2)(3 in)(8.41 in) = 12.615 in²
V = (1/3)(12.615 in²)(8.41 in) = 33.49 in³
The volume of the triangular prism is given by the formula V = Bh, where B is the area of the triangular base and h is the height of the prism.
Substituting the values given, we get:
B = (1/2)(3 in)(8.41 in) = 12.615 in²
V = (12.615 in²)(8.41 in) = 105.83 in³
Comparing these volumes, we can see that the prism has a larger volume than the pyramid.
The prism is larger by a factor of 105.83 in³ / 33.49 in³, which simplifies to approximately 3.16 times.
Answer: The prism has a larger volume by three times (approximately 3.16 times).
An illustration shows a triangular pyramid and a triangular prism. The edges that are not visible are marked as dashed lines. The triangular pyramid has the triangular face as its base. The sides of of the triangular base measure 3 inches and 5 inches. The perpendicular height of the pyramid is 8.41 inches. The triangular prism has its triangular face as the base. The sides of the triangular base measure 3 inches and 5 inches. The length of the side is 8.41 inches.
Which shape has the larger volume? How much larger is it?
The pyramid has a larger volume by three times.
The volumes are the same.
The prism has a larger volume by 1/3 times.
The prism has a larger volume by three times.
The prism has a larger volume by three times.
Use the image to answer the question.
An illustration shows a triangle with its base as 20 feet and its perpendicular height as 6 feet.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft.3, what is the volume of the pyramid?
600 ft.3
200 ft.3
400 ft.3
1,800 ft.3
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.
In this case, the base is a triangle with a base of 20 feet and a perpendicular height of 6 feet.
The area of the triangle base is:
B = (1/2)bh = (1/2)(20 ft)(6 ft) = 60 sq ft
The given volume of the prism is 600 cubic feet.
Therefore, we can solve for the height of the prism as follows:
V = Bh
600 ft.³ = 60 sq ft x h
h = 10 ft
So, the height of both the prism and the pyramid is 10 feet.
Now, the volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the triangular base and h is the height of the pyramid.
Since the triangular base of the pyramid is the same as that of the prism, its area is also 60 sq ft, and its height is 10 ft.
Therefore, the volume of the pyramid is:
V = (1/3)Bh = (1/3)(60 sq ft)(10 ft) = 200 cubic feet
So, the volume of the pyramid is 200 cubic feet.
Answer: 200 ft.³
Use the image to answer the question.
An illustration shows a rectangular prism with a cube placed on top. The cube is 3 inches on all sides. The rectangular prism is 11 inches long and 4 inches high.
What is the volume of the composite figure?
? in.3
To find the volume of the composite figure, we need to add the volumes of the rectangular prism and the cube.
The volume of the rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism.
Substituting the given values, we get:
V = (11 in) x (3 in) x (4 in) = 132 cubic inches
The volume of the cube is given by the formula V = s^3, where s is the length of a side of the cube.
Substituting the given value, we get:
V = (3 in)^3 = 27 cubic inches
Therefore, the volume of the composite figure is:
V = volume of prism + volume of cube = 132 cubic inches + 27 cubic inches = 159 cubic inches
So, the volume of the composite figure is 159 cubic inches.
Answer: 159 in³.
Use the image to answer the question.
An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long.
What is the volume of the composite figure?
(1 point)
To find the volume of the composite figure, we need to add the volumes of the three rectangular prisms.
Volume of the side rectangular prism = lwh = (16 in)(7 in)(7 in) = 784 cubic inches
Volume of the center rectangular prism = lwh = (10 in)(8 in)(7 in) = 560 cubic inches
Therefore, the total volume of the composite figure is:
Total volume = Volume of the side rectangular prism + 2 × Volume of the center rectangular prism
Total volume = 784 cubic inches + 2 × 560 cubic inches
Total volume = 1,904 cubic inches
So, the volume of the composite figure is 1,904 cubic inches.
Answer: 1,904 in³.
Use the image to answer the question.
An illustration shows a center-pedestal type table with the table top placed on vertical rectangular block that has a rectangular base. The table top length and width are 30 inches, with a depth of 2 inches. The height of the rectangular block pedestal is 25 inches, and the width and length are 8 inches each. The length and width of the rectangular base are 12 inches each, and the height is 4 inches. The table top has a checkerboard pattern.
What is the volume of the table?
To find the volume of the table, we need to calculate the volumes of the table top and the rectangular block.
Volume of the table top can be divided into smaller units with dimensions of 3 in by 3 in by 2 in. So, the space between any two consecutive boards is 1 inch (3 in - 2 in).
The table top is made up of 15 rows of 5 squares each, and each square has a volume of:
V1 = 3 in x 3 in x 2 in = 18 cubic inches
The number of squares with a height of 2 inches is 15 * 5 = 75.
The total volume of the parts with a height of 2 inches is:
V2 = 75 * 18 cubic inches = 1,350 cubic inches
Therefore, the volume of the table top is:
Vtop = V1 + V2 = 18 cubic inches + 1,350 cubic inches = 1,368 cubic inches
The volume of the rectangular block can be calculated as:
Vblock = lwh = (8 in)(8 in)(25 in) = 1,600 cubic inches
The volume of the rectangular base can be calculated as:
Vbase = lwh = (12 in)(12 in)(4 in) = 576 cubic inches
Therefore, the total volume of the table is:
Vtable = Vtop + Vblock + Vbase
Vtable = 1,368 cubic inches + 1,600 cubic inches + 576 cubic inches
Vtable = 3,544 cubic inches
Therefore, the volume of the table is 3,544 cubic inches.
Answer: 3,544 in³.