describe the two dimensional figure that results from slicing right rectangular pyramids perpendicular to the base through the Apex
The volume of the rectangular pyramid can be found using the formula:
V = (1/3)Bh
where B is the area of the rectangular base, and h is the height of the pyramid.
The area of the rectangular base is:
A = lw = (4 cm) × (9 cm) = 36 cm²
Substituting the given values, we have:
V = (1/3)(36 cm²)(21 cm)
V = 252 cm³
Therefore, the volume of the piece of cheese is 252 cubic centimeters.
Answer: 252 cm³.
The volume of a rectangular prism is given by the formula:
V_prism = lwh
We know that the volume of the rectangular prism is 27 inches cubed, so:
27 = lwh
The rectangular pyramid has the same base and height as the rectangular prism, so its volume is one third of the volume of the prism:
V_pyramid = (1/3
When a right rectangular pyramid is sliced perpendicular to the base through the apex, the resulting two-dimensional shape is a triangle. The triangle is isosceles, with two equal sides that are perpendicular to the base of the pyramid. The third side is the line formed by the intersection of the pyramid and the plane of the cut. The angle between the two equal sides depends on the angle between the edges of the pyramid and the base.
Describe the two-dimensional figure that results from slicing right rectangular pyramids perpendicular from the side.(1 point)
Responses
hexagon
hexagon
triangle
triangle
square
square
trapezoid
trapezoid
What is the two-dimensional shape created by slicing a rectangular pyramid from the side?
(1 point)
Responses
trapezoid
trapezoid
triangle
triangle
square
square
rectangle
trapezoid
After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
Responses
square and triangle
square and triangle
triangles
triangles
rectangle and triangles
rectangle and triangles
rectangles
rectangles
rectangles and triangles
What is the slant height in a rectangular or square pyramid?(1 point)
Responses
the height of the pyramid from the apex straight down to the middle of the base of the pyramid
the height of the pyramid from the apex straight down to the middle of the base of the pyramid
the distance across the triangular face
the distance across the triangular face
the height from the apex straight down to the base of the triangular face where it forms a right angle
the height from the apex straight down to the base of the triangular face where it forms a right angle
an edge of a triangular face
the height from the apex straight down to the base of the triangular face where it forms a right angle
What is a two-dimensional representation of a three-dimensional figure?(1 point)
Responses
a square
a square
a rectangle
a rectangle
a cube
a cube
a net
a net
a net
What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2?
One way to solve the problem is to use the formula for surface area of a rectangular prism:
S = 2lw + 2lh + 2wh
where S is the surface area, l is the length, w is the width, and h is the height.
Substituting the given values, we have:
432 = 2(l)(9) + 2(9)(9) + 2(w)(9)
Simplifying:
432 = 18l + 162 + 18w
Dividing both sides by 18:
24 = l + w
Since we know that the height and width are both 9 cm, we can substitute 9 for both w and h:
24 = l + 9
Subtracting 9 from both sides:
15 = l
Therefore, the missing length is 15 cm.
Fill in the blanks to complete the formula for the surface area of a triangular prism. (1 point)
The surface area of a triangular prism is S.A.=
+(S1+S2+S3)
2B
Jerry wants to wrap a present in a box for his mother. The box measures 10 cm wide, 4 cm high, and 17 cm long. How much wrapping paper will Jerry need to wrap the present?
To determine the amount of wrapping paper needed to wrap a present, we need to find the surface area of the box. The surface area is the sum of the area of each face, so we can use the formula:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width and height of the box, respectively.
Substituting the given values, we have:
Surface area = 2(17)(10) + 2(17)(4) + 2(10)(4)
Surface area = 340 + 136 + 80
Surface area = 556
Therefore, Jerry will need 556 square centimeters of wrapping paper to wrap the present.
What is the shape of the base of a rectangular pyramid?(1 point)
Responses
vertex
vertex
pyramid
pyramid
rectangle
rectangle
triangle
rectangle
Solve the problem. The surface area of a square pyramid is 116 in.2 and the total area of the pyramid’s four triangular faces is 80 in.2
What is the length of one of the sides? Show your work.
Let's denote the length of one side of the square base of the pyramid as s, and the slant height as l. We need to find the length of s.
The surface area of the square pyramid is given by:
116 in² = s² + 4(1/2)(s)(l)
where the first term on the right-hand side is the area of the square base and the second term is the sum of the areas of the four triangular faces.
The total area of the four triangular faces is given as 80 in²:
80 in² = 4(1/2)(s)(l)
Now we have two equations with two unknowns. Rearranging the second equation, we have:
l = 40 / s
Substituting this expression for l into the first equation and simplifying, we obtain:
116 = s² + 4s(40/s)
116 = s² + 160
Solving for s, we have:
s² = -44
This is not a valid solution for s, since the length of a side must be positive.
Therefore, there is no real solution for the length of one of the sides of the square pyramid with the given information.
Solve the problem. The surface area of a square pyramid is 116 square inches and the total area of the pyramid’s four triangular faces is 80 square inches
What is the length of one of the sides? Show your work.
Let's denote the length of one side of the square base of the pyramid as s, and the slant height as l. We need to find the length of s.
The surface area of the square pyramid is given by:
116 in² = s² + 4(1/2)(s)(l)
where the first term on the right-hand side is the area of the square base and the second term is the sum of the areas of the four triangular faces.
The total area of the four triangular faces is given as 80 in²:
80 in² = 4(1/2)(s)(l)
Simplifying the second equation, we have:
20 in² = s l
Rearranging this equation, we get:
l = 20 / s
Substituting this expression for l into the first equation and simplifying, we obtain:
116 = s² + 4s(20/s)
116 = s² + 80
Solving for s, we have:
s² = 36
Therefore, s = 6 in.
So the length of one of the sides of the square pyramid is 6 inches.
Eduardo has a 32-gallon fish tank. Describe what this measurement means.(1 point)
Responses
It means his fish tank is 32 feet long.
It means his fish tank is 32 feet long.
It means his fish tank holds 32 gallons of water.
It means his fish tank holds 32 gallons of water.
It means his fish tank holds 32 fish.
It means his fish tank holds 32 fish.
It means his fish tank is too big.
It means his fish tank holds 32 gallons of water.
Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point)
Responses
33,034.03 in.3
33,034.03 in. cubed
400,000 in.3
400,000 in. cubed
308,025 in.3
308,025 in. cubed
924,075 in.3
308,025 in.3
A cell phone telecommunication tower stands in the shape of a rectangular pyramid. The tower stands 80 m tall and rests on a base that is 15 m by 20 m. What is the volume of the tower?(1 point)
Responses
8,000 m3
8,000 m cubed
70 m3
, 70 m cubed
12,000 m3
, 12,000 m cubed
24,000 m3
, 24,000 m cubed
The volume of the rectangular pyramid can be found using the formula:
V = (1/3)Bh
where B is the area of the rectangular base, h is the height of the pyramid.
The area of the rectangular base is:
A = lw = 15m x 20m = 300 m^2
Substituting the given values, we have:
V = (1/3)(300 m^2)(80 m)
V = 8,000 m^3
Therefore, the volume of the cell phone telecommunication tower is 8,000 cubic meters.
Answer: 8,000 m^3.
A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.(1 point)
Responses
20.80 in.3
, 20.80 in. cubed
9.01 in.3
, 9.01 in. cubed
6.93 in.3
6.93 in. cubed
24.47 in.3
The volume of the square pyramid ornament can be found using the formula:
V = (1/3)Bh
where B is the area of the square base, h is the height of the pyramid.
The area of the square base is:
A = s^2 = (2.75 in)^2 = 7.5625 in^2
Substituting the given values, we have:
V = (1/3)(7.5625 in^2)(2.75 in)
V = 6.91797 in^3
Rounding to the nearest hundredth, the volume is approximately:
V ≈ 6.92 in^3
Therefore, the approximate volume of the ornament is 6.92 cubic inches.
Answer: 6.92 in^3.
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3, what is the volume of the prism?(1 point)
Responses
96 in.3
, 96 in. cubed
24 in.3
, 24 in. cubed
16 in.3
, 16 in. cubed
144 in.3
If the rectangular prism and the pyramid have congruent bases and heights, then the volume of the prism is three times the volume of the pyramid (since the prism has three congruent pyramids).
Therefore, the volume of the rectangular prism is:
V_prism = 3(48 in^3) = 144 in^3
Therefore, the volume of the rectangular prism is 144 cubic inches.
Answer: 144 in^3.
A rectangular prism has a base area of 15 cm2, and a congruent pyramid has a volume of 20 cm3. What is the height of the rectangular prism?(1 point)
Responses
20 cm
, 20 cm
43 cm
, Start Fraction 4 over 3 End Fraction cm
4 cm
4 cm
5 cm
If the rectangular prism has a base area of 15 cm^2, then the length times the width of the base must be 15 cm^2. We can set up an equation using the formula for the volume of a rectangular prism:
V_prism = Bh
where B is the area of the base, and h is the height of the prism.
Using the given information, we have:
15h = V_prism
Since we don't know the height of the prism, let's call it x. If the pyramid is congruent with the base of the prism, then its volume must be one third of the volume of the prism:
V_pyramid = (1/3)Bx = 20 cm^3
Substituting B = 15 cm^2 and solving for x, we get:
(1/3)(15 cm^2)x = 20 cm^3
5x = 60
x = 12 cm
Therefore, the height of the rectangular prism is 12 cm.
Answer: 12 cm.
A rectangular prism has a base area of 15 cm2, and a congruent pyramid has a volume of 20 cm3. What is the height of the rectangular prism?
If the rectangular prism has a base area of 15 cm², then the length times the width of the base must be 15 cm². We can set up an equation using the formula for the volume of a rectangular prism:
V = Bh
where B is the area of the base, and h is the height of the prism.
Using the given information, we have:
15h = V
Since we don't know the height of the prism, let's call it x. If the pyramid is congruent with the base of the prism, then its volume must be one-third of the volume of the prism:
V_pyramid = (1/3)Bx = 20 cm³
Substituting B = 15 cm² and solving for x, we get:
(1/3)(15 cm²)x = 20 cm³
5x = 60
x = 12 cm
Therefore, the height of the rectangular prism is 12 cm.
Answer: 12 cm.
A rectangular prism has a base area of 15 cm squared, and a congruent pyramid has a volume of 20 cm cubed. What is the height of the rectangular prism?
If the rectangular prism has a base area of 15 cm², then the length times the width of the base must be 15 cm². We can set up an equation using the formula for the volume of a rectangular prism:
V_prism = Bh
where B is the area of the base, and h is the height of the prism.
Using the given information, we have:
15h = V_prism
Since we don't know the height of the prism, let's call it x. If the pyramid is congruent with the base of the prism, then its volume must be one-third of the volume of the prism:
V_pyramid = (1/3)Bx = 20 cm³
Substituting B = 15 cm² and solving for x, we get:
(1/3)(15 cm²)x = 20 cm³
5x = 60
x = 12 cm
Therefore, the height of the rectangular prism is 12 cm.
Answer: 12 cm.
A farmer is building a storage barn that must hold 33,000 cubic feet of hay. Which choice best describes what this means?(1 point)
Responses
This size of barn is impossible to build.
This size of barn is impossible to build.
The barn must have enough capacity for 33,000 cubic feet of hay.
The barn must have enough capacity for 33,000 cubic feet of hay.
The barn must be 33,000 feet long.
The barn must be 33,000 feet long.
The farmer does not have enough space to build this barn.
The farmer does not have enough space to build this barn.
The farmer must build a barn that has enough capacity for 33,000 cubic feet of hay.
Answer: The barn must have enough capacity for 33,000 cubic feet of hay.
If the volume of a right rectangular prism is 1.5 inches cubed and its length and width have a product of 1.5 inches squared, what is the height of this prism?
Let's call the length of the rectangular prism "l", its width "w", and its height "h".
We know that the volume V is 1.5 inches cubed:
V = lwh = 1.5
We also know that the product of the length and width is 1.5 inches squared:
lw = 1.5
We can use the second equation to solve for one of the variables, for example:
w = 1.5/l
Substituting this expression into the first equation, we can solve for h:
V = lwh = 1.5
V/l = hw
h = V/(lw) = 1.5/(l*(1.5/l)) = 1 in.
Therefore, the height of the rectangular prism is 1 inch.
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?
A rectangular prism has a volume of 27 inches squared. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
sorry i meant
A rectangular prism has a volume of 27 inches cubed. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?