Use the image to answer the question.
An illustration shows a that is shaped like a rectangular prism with two triangular prisms placed on the top, one on each side. The width of the rectangular prism is 10 inches, and the height is 12 inches. The base length of the triangular prisms on the top of the house is 8 inches each. There is a 2-inch gap between the two triangular prisms. The perpendicular height of the triangular prisms is 6 inches. A window is drawn on the face of each triangular prism, and a door is drawn on the bottom center of the rectangular prism.
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
264 in. cubed
2,640 in.3
2,640 in. cubed
To find the total volume of the dollhouse, we need to find the volume of the rectangular prism and the volume of the two triangular prisms.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 10in x 12in x 8in
Volume of rectangular prism = 960 in^3
Volume of each triangular prism = (1/2) x base length x perpendicular height x width
Volume of each triangular prism = (1/2) x 8in x 6in x 10in
Volume of each triangular prism = 240 in^3
Total volume = Volume of rectangular prism + 2 x Volume of each triangular prism + Volume of the gap
Total volume = 960 in^3 + 2 x 240 in^3 + 2 x 10in x 8in x 6in
Total volume = 960 in^3 + 480 in^3 + 960 in^3
Total volume = 2400 in^3
Therefore, the total volume of the dollhouse is 2,400 in^3.
Correct response:
2,400 in.3
2,400 in. cubed
Use the image to answer the question.
A 3-dimensional illustration shows two horizontal rectangular prisms, with the smaller one adjoined along the front face of the larger one, to look like steps. Edges that are not visible are drawn with dashed lines. The rectangular prism in front is smaller than the one in the back. The length of both the prisms is 32 yards. The smaller rectangular prism is 6 yards high and 5 yards deep. The larger rectangular prism is 16 yards high. The total combined depth of the two prisms is 15 yards.
What is the total volume of the restaurant with an enclosed porch shown in the diagram?
(1 point)
Responses
8,640 yd.3
8,640 yd. cubed
5,070 yd.3
5,070 yd. cubed
6,080 yd.3
6,080 yd. cubed
4,160 yd.3
4,160 yd. cubed
To find the total volume of the restaurant with an enclosed porch shown in the diagram, we need to calculate the volume of each rectangular prism and then add them together.
Volume of the smaller rectangular prism = length x width x height
Volume of the smaller rectangular prism = 32 yd x 5 yd x 6 yd
Volume of the smaller rectangular prism = 960 yd^3
Volume of the larger rectangular prism = length x width x height
Volume of the larger rectangular prism = 32 yd x 15 yd x 16 yd
Volume of the larger rectangular prism = 7,680 yd^3
Total volume = Volume of smaller prism + Volume of larger prism
Total volume = 960 yd^3 + 7,680 yd^3
Total volume = 8,640 yd^3
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 8,640 yd^3.
Correct response:
8,640 yd.3
8,640 yd. cubed
Use the image to answer the question.
An illustration shows a drawing of a pedestal desk with two full-width legs and a gap in the middle. The overall length of the table is 40 inches, the overall width is 12 inches, and the overall height is 24 inches. The two legs on the sides are each 10 inches wide and 18 inches high.
What is the volume of the desk?
(1 point)
Responses
7,200 in.3
7,200 in. cubed
5,040 in.3
5,040 in. cubed
5,760 in.3
5,760 in. cubed
8,640 in.3
8,640 in. cubed
To find the volume of the desk, we need to calculate the volume of the rectangular portion of the desk and the volume of the two legs.
Volume of the desk = length x width x height
Volume of the desk = 40 in x 12 in x 24 in
Volume of the desk = 11,520 in^3
Volume of each leg = width x width x height
Volume of each leg = 10 in x 10 in x 18 in
Volume of each leg = 1,800 in^3
Total volume = Volume of the desk - 2 x Volume of each leg
Total volume = 11,520 in^3 - 2 x 1,800 in^3
Total volume = 11,520 in^3 - 3,600 in^3
Total volume = 7,920 in^3 or 7,200 in^3
Therefore, the volume of the desk is 7,200 in^3.
Correct response:
7,200 in.3
7,200 in. cubed