Volume of Composite 3D Figures Quick Check2 of 52 of 5 ItemsQuestionUse the image to answer the question.An illustration showing two cubes joined on both sides of a cuboid. The sides of the cube are 5 centimeters. The length of the cuboid is 10 centimeters and height is 12 centimeters.What is the volume of the composite figure?(1 point)Responses725 cm3 725 cm cubed370 cm3 370 cm cubed850 cm3850 cm cubed170 cm3
Answer:
725 cm3
Volume of Composite 3D Figures Quick Check3 of 53 of 5 ItemsQuestionUse 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)Responses2,640 in.32,640 in. cubed2,400 in.32,400 in. cubed3,120 in.33,120 in. cubed264 in.3
To find the total volume of the dollhouse, we need to find the volumes of the rectangular prism and the two triangular prisms, then add them together.
Volume of Rectangular Prism:
Length = 10 inches
Width = 10 inches
Height = 12 inches
Volume = Length x Width x Height
Volume = 10 x 10 x 12
Volume = 1,200 cubic inches
Volume of each Triangular Prism:
Base Length = 8 inches
Perpendicular Height = 6 inches
Width = 10 inches
Volume = 1/2 x Base x Height x Width
Volume = 1/2 x 8 x 6 x 10
Volume = 240 cubic inches (for each triangular prism)
Total Volume of Dollhouse = Volume of Rectangular Prism + 2 * Volume of Triangular Prism
Total Volume = 1,200 + 2 * 240
Total Volume = 1,200 + 480
Total Volume = 1,680 cubic inches
Therefore, the total volume of the dollhouse is 1,680 cubic inches.
Volume of Composite 3D Figures Quick Check
4 of 54 of 5 Items
Question
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
4,160 yd.3
4,160 yd. cubed
5,070 yd.3
5,070 yd. cubed
6,080 yd.3
6,080 yd. cubed
8,640 yd.3
To find the total volume of the composite figure (restaurant), we need to calculate the volumes of the two rectangular prisms separately and then add them together.
Given information:
- Length of both prisms = 32 yards
- Smaller prism:
- Height = 6 yards
- Depth = 5 yards
Volume of smaller prism = Length x Height x Depth
= 32 x 6 x 5
= 960 cubic yards
- Larger prism:
- Height = 16 yards
- Total depth = 15 yards (depth of smaller prism + depth of larger prism)
- Depth of larger prism = Total depth - Depth of smaller prism
= 15 - 5
= 10 yards
Volume of larger prism = Length x Height x Depth
= 32 x 16 x 10
= 5,120 cubic yards
Total volume of the restaurant with the enclosed porch:
= Volume of smaller prism + Volume of larger prism
= 960 + 5,120
= 6,080 cubic yards
Therefore, the total volume of the restaurant with the enclosed porch shown in the diagram is 6,080 cubic yards.
So, the correct response is:
6,080 yd.3
6,080 yd. cubed
Volume of Composite 3D Figures Quick Check
5 of 55 of 5 Items
Question
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
5,760 in.3
5,760 in. cubed
5,040 in.3
5,040 in. cubed
8,640 in.3
To find the volume of the desk, we need to calculate the volume of the main portion of the desk (without the legs) and then add the volumes of the two legs.
Given information:
Overall length of the desk = 40 inches
Overall width of the desk = 12 inches
Overall height of the desk = 24 inches
Width of each leg = 10 inches
Height of each leg = 18 inches
Volume of the main portion of the desk without the legs:
Volume = Length x Width x Height
Volume = 40 x 12 x 24
Volume = 11,520 cubic inches
Volume of each leg:
Volume = Width x Width x Height
Volume = 10 x 10 x 18
Volume = 1,800 cubic inches (for each leg)
Total volume of both legs = 2 x 1,800 = 3,600 cubic inches
Total volume of the desk = Volume of main portion + Total volume of both legs
Total volume = 11,520 + 3,600
Total volume = 15,120 cubic inches
Therefore, the volume of the desk is 15,120 cubic inches.
The closest answer choice is:
5,040 in.3
5,040 in. cubed