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?
? in.3
To find the volume of the composite figure, we need to find the volume of each rectangular prism and add them together.
Volume of one side prism:
V = lwh = 16 x 7 x 7 = 784 in.3
Volume of center prism:
V = lwh = 10 x 8 x 7 = 560 in.3
Total volume of composite figure:
(2 x 784) + 560 = 2,128 in.3
Therefore, the volume of the composite figure is 2,128 in.3.
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?
? in.3
To find the volume of the table, we need to calculate the volume of each component and then add them together.
Volume of table top:
V = lwh = 30 x 2 x 30 = 1800 in.3
Volume of rectangular block pedestal:
V = lwh = 8 x 8 x 25 = 1600 in.3
Volume of rectangular base:
V = lwh = 12 x 12 x 4 = 576 in.3
Total volume of the table:
1800 + 1600 + 576 = 3976 in.3
Therefore, the volume of the table is 3976 in.3.
An illustration shows the composite structure of a movie theater that is formed with a large square prism in the middle with four smaller square prisms extending from the four sides. The entire structure is 20 meters in height. The square prism in the center measures 44 meters on each side. The smaller square prisms extend outward from the center of each side. The smaller square prisms are 15 meters on each side. A sign labeled Movies sits on the top of the structure.
What is the volume of the movie theater?
? m3
To find the volume of the movie theater, we need to calculate the volumes of each individual component and then add them together.
Volume of the center square prism:
V = l^2h = 44^2 x 20 = 38,720 m^3
Volume of one of the smaller square prisms:
V = l^2h = 15^2 x 20 = 4,500 m^3
Since there are four of these, we multiply the result by 4:
4,500 x 4 = 18,000 m^3
Total volume of the movie theater:
38,720 + 18,000 = 56,720 m^3
Therefore, the volume of the movie theater is 56,720 m^3.
Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.
The formula for the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
Substituting the given values, we get:
V = (1/3)(200)(75)
Simplifying:
V = 5,000
Therefore, the volume of the rectangular pyramid is 5,000 cubic meters.
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a right triangular prism placed on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 feet and a height of 8 feet. The width of the rectangular prism is not shown. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
____ft.2
To find the surface area of the composite figure, we need to calculate the surface area of each individual component and then add them together.
Surface area of the rectangular prism:
There are two identical rectangular faces with dimensions 12 ft x 8 ft, so the total surface area is:
2(12 x 8) = 192 ft^2
There are also two identical faces hidden from view. Since we don't have the width dimension, we can assume that the width is also 8 ft. Thus, the surface area of each hidden face is:
8 x h, where h is the height of the rectangular prism (which is not given). Since we know that the total height of the left side of the figure is 20 feet, we can use this to solve for the height of the rectangular prism.
20 = 8 + h
h = 12 ft
So the total surface area of the hidden faces is:
2(8 x 12) = 192 ft^2
Surface area of the right triangular prism:
The right triangular prism has a width of 8 ft and a hypotenuse of 15 ft. We can use the Pythagorean theorem to find the length of the other two sides:
a^2 + b^2 = c^2
a^2 + 8^2 = 15^2
a^2 = 15^2 - 8^2
a^2 = 161
a ≈ 12.68
So the right triangular prism has a base area of:
(1/2)(12.68 ft)(8 ft) = 50.72 ft^2
The three visible faces of the right triangular prism are rectangles with dimensions 8 ft x h, where h is the height of the right triangular prism (which is not given). Since the edges of the right triangular prism align perfectly with the edges of the top rectangular face, the height of the right triangular prism is the same as the height of the rectangular prism:
h = 12 ft
So the total surface area of the visible faces of the right triangular prism is:
3(8 x 12) = 288 ft^2
Total surface area:
Adding up all of the surface areas, we get:
192 + 192 + 50.72 + 288 = 722.72 ft^2
Therefore, the surface area of the composite figure is approximately 722.72 square feet.