To find the total volume of the dollhouse, we need to calculate the volume of the rectangular prism base and the volume of the two triangular prisms on top.
Volume of the rectangular prism base:
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 one triangular prism:
Base length = 8 inches
Perpendicular height = 6 inches
Width = 10 inches
Volume = (1/2) x Base length x Perpendicular height x Width
Volume = (1/2) x 8 x 6 x 10
Volume = 240 cubic inches
Total volume of both triangular prisms:
Volume = 2 x 240 = 480 cubic inches
Total volume of the dollhouse:
Total Volume = Volume of the rectangular prism base + Total volume of both triangular prisms
Total Volume = 1,200 + 480
Total Volume = 1,680 cubic inches
Therefore, the total volume of the dollhouse is 1,680 cubic inches.
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)Responses2,640 in.32,640 in. cubed3,120 in.33,120 in. cubed2,400 in.32,400 in. cubed264 in.3
9 answers
Write and solve an expression for the total volume of the dollhouse.(1 point)Responses2,640 in.32,640 in. cubed3,120 in.33,120 in. cubed2,400 in.32,400 in. cubed264 in.3
Total volume of the dollhouse can be calculated by adding the volume of the rectangular prism base and the total volume of both triangular prisms.
Volume of the rectangular prism base:
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 one triangular prism:
Base length = 8 inches
Perpendicular height = 6 inches
Width = 10 inches
Volume = (1/2) x Base length x Perpendicular height x Width
Volume = (1/2) x 8 x 6 x 10
Volume = 240 cubic inches
Total volume of both triangular prisms:
Volume = 2 x 240 = 480 cubic inches
Therefore, the total expression for the volume of the dollhouse is:
1,200 (volume of rectangular prism base) + 480 (total volume of both triangular prisms)
1,200 + 480 = 1,680 cubic inches
So, the total volume of the dollhouse is 1,680 cubic inches.
The correct response is: 1,680 in.3
Volume of the rectangular prism base:
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 one triangular prism:
Base length = 8 inches
Perpendicular height = 6 inches
Width = 10 inches
Volume = (1/2) x Base length x Perpendicular height x Width
Volume = (1/2) x 8 x 6 x 10
Volume = 240 cubic inches
Total volume of both triangular prisms:
Volume = 2 x 240 = 480 cubic inches
Therefore, the total expression for the volume of the dollhouse is:
1,200 (volume of rectangular prism base) + 480 (total volume of both triangular prisms)
1,200 + 480 = 1,680 cubic inches
So, the total volume of the dollhouse is 1,680 cubic inches.
The correct response is: 1,680 in.3
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
2,640 in.3
2,640 in. cubed
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
Responses
2,640 in.3
2,640 in. cubed
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
The total volume of the dollhouse can be found by adding the volume of the rectangular prism base and the total volume of both triangular prisms.
Volume of the rectangular prism base:
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 one triangular prism:
Base length = 8 inches
Perpendicular height = 6 inches
Width = 10 inches
Volume = (1/2) x Base length x Perpendicular height x Width
Volume = (1/2) x 8 x 6 x 10
Volume = 240 cubic inches
Total volume of both triangular prisms:
Volume = 2 x 240 = 480 cubic inches
Therefore, the total expression for the volume of the dollhouse is:
1,200 (volume of rectangular prism base) + 480 (total volume of both triangular prisms)
1,200 + 480 = 1,680 cubic inches
The correct response based on the given options is:
2,400 in. cubed
Volume of the rectangular prism base:
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 one triangular prism:
Base length = 8 inches
Perpendicular height = 6 inches
Width = 10 inches
Volume = (1/2) x Base length x Perpendicular height x Width
Volume = (1/2) x 8 x 6 x 10
Volume = 240 cubic inches
Total volume of both triangular prisms:
Volume = 2 x 240 = 480 cubic inches
Therefore, the total expression for the volume of the dollhouse is:
1,200 (volume of rectangular prism base) + 480 (total volume of both triangular prisms)
1,200 + 480 = 1,680 cubic inches
The correct response based on the given options is:
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)Responses8,640 yd.38,640 yd. cubed6,080 yd.36,080 yd. cubed5,070 yd.35,070 yd. cubed4,160 yd.34,160 yd. cubed
To find the total volume of the restaurant with the enclosed porch, we need to calculate the volume of each rectangular prism individually and then sum them up.
Volume of the smaller rectangular prism:
Length = 32 yards
Height = 6 yards
Depth = 5 yards
Volume = Length x Height x Depth
Volume = 32 x 6 x 5
Volume = 960 cubic yards
Volume of the larger rectangular prism:
Length = 32 yards
Height = 16 yards
Depth = Total combined depth - Depth of smaller prism
Depth of larger prism = Total combined depth - Depth of smaller prism = 15 - 5 = 10 yards
Volume = Length x Height x Depth
Volume = 32 x 16 x 10
Volume = 5,120 cubic yards
Total volume of the restaurant with the enclosed porch:
Total Volume = Volume of the smaller prism + Volume of the larger prism
Total Volume = 960 + 5,120
Total Volume = 6,080 cubic yards
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 6,080 cubic yards.
The correct response is:
6,080 yd. cubed
Volume of the smaller rectangular prism:
Length = 32 yards
Height = 6 yards
Depth = 5 yards
Volume = Length x Height x Depth
Volume = 32 x 6 x 5
Volume = 960 cubic yards
Volume of the larger rectangular prism:
Length = 32 yards
Height = 16 yards
Depth = Total combined depth - Depth of smaller prism
Depth of larger prism = Total combined depth - Depth of smaller prism = 15 - 5 = 10 yards
Volume = Length x Height x Depth
Volume = 32 x 16 x 10
Volume = 5,120 cubic yards
Total volume of the restaurant with the enclosed porch:
Total Volume = Volume of the smaller prism + Volume of the larger prism
Total Volume = 960 + 5,120
Total Volume = 6,080 cubic yards
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 6,080 cubic yards.
The correct response is:
6,080 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)Responses8,640 in.38,640 in. cubed5,040 in.35,040 in. cubed7,200 in.37,200 in. cubed5,760 in.3
To find the volume of the desk, we first need to calculate the volume of the rectangular portion of the desk, excluding the legs, and then add the volume of both legs.
Volume of the rectangular portion of the desk:
Length = 40 inches
Width = 12 inches
Height = 24 inches
Volume = Length x Width x Height
Volume = 40 x 12 x 24
Volume = 11,520 cubic inches
Volume of one leg:
Width = 10 inches
Height = 18 inches
Depth (same as depth of the desk) = 12 inches
Volume = Width x Height x Depth
Volume = 10 x 18 x 12
Volume = 2,160 cubic inches
Volume of both legs:
Total volume of legs = 2 x Volume of one leg
Total volume of legs = 2 x 2,160
Total volume of legs = 4,320 cubic inches
Total volume of the desk:
Total volume = Volume of the rectangular portion + Total volume of legs
Total volume = 11,520 + 4,320
Total volume = 15,840 cubic inches
Therefore, the volume of the desk is 15,840 cubic inches.
The correct response is:
15,840 in.3
Volume of the rectangular portion of the desk:
Length = 40 inches
Width = 12 inches
Height = 24 inches
Volume = Length x Width x Height
Volume = 40 x 12 x 24
Volume = 11,520 cubic inches
Volume of one leg:
Width = 10 inches
Height = 18 inches
Depth (same as depth of the desk) = 12 inches
Volume = Width x Height x Depth
Volume = 10 x 18 x 12
Volume = 2,160 cubic inches
Volume of both legs:
Total volume of legs = 2 x Volume of one leg
Total volume of legs = 2 x 2,160
Total volume of legs = 4,320 cubic inches
Total volume of the desk:
Total volume = Volume of the rectangular portion + Total volume of legs
Total volume = 11,520 + 4,320
Total volume = 15,840 cubic inches
Therefore, the volume of the desk is 15,840 cubic inches.
The correct response is:
15,840 in.3
3 answers