To find the volume of the composite figure, we first need to find the volume of the rectangular prism and then add the volume of the cube.
Volume of the rectangular prism:
Length = 6 inches
Width = 6 inches
Height = 2 inches
Volume = Length x Width x Height
Volume = 6 x 6 x 2
Volume = 72 cubic inches
Volume of the cube:
Side length = 2 inches
Volume = Side length^3
Volume = 2^3
Volume = 8 cubic inches
Total volume of the composite figure:
Volume = Volume of the rectangular prism + Volume of the cube
Volume = 72 + 8
Volume = 80 cubic inches
Therefore, the volume of the composite figure is 80 cubic inches.
Use the image to answer the question.An illustration shows a cube placed on the top and center of a larger rectangular prism. The length and width of the prism is 6 inches respectively and 2 inches high. The sides of the cube are 2 inches.What is the volume of the composite figure?(1 point)
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Use the image to answer the question.An illustration shows a rectangular prism, placed vertically, on the top corner of a larger cube. The length and width of the prism is 1 foot respectively and the height is 3 feet. The sides of the cube are 3 feet.What is the volume of the composite figure?(1 point) ft.3
To find the volume of the composite figure in this case, we need to find the combined volume of the rectangular prism and the cube.
Volume of the rectangular prism:
Length = 1 foot
Width = 1 foot
Height = 3 feet
Volume = Length x Width x Height
Volume = 1 x 1 x 3
Volume = 3 cubic feet
Volume of the cube:
Side length = 3 feet
Volume = Side length^3
Volume = 3^3
Volume = 27 cubic feet
Total volume of the composite figure:
Volume = Volume of the rectangular prism + Volume of the cube
Volume = 3 + 27
Volume = 30 cubic feet
Therefore, the volume of the composite figure is 30 cubic feet.
Volume of the rectangular prism:
Length = 1 foot
Width = 1 foot
Height = 3 feet
Volume = Length x Width x Height
Volume = 1 x 1 x 3
Volume = 3 cubic feet
Volume of the cube:
Side length = 3 feet
Volume = Side length^3
Volume = 3^3
Volume = 27 cubic feet
Total volume of the composite figure:
Volume = Volume of the rectangular prism + Volume of the cube
Volume = 3 + 27
Volume = 30 cubic feet
Therefore, the volume of the composite figure is 30 cubic feet.
Use the image to answer the question.An illustration shows two cubes joined on both sides of a cuboid. The sides of the cube are 2 yards. The length of the cuboid is 4.5 yards.What is the volume of the composite figure?(1 point)
To find the volume of the composite figure made up of two cubes joined on both sides of a cuboid, we need to calculate the volumes of the two cubes and the cuboid and then add them together.
Volume of one cube:
Side length = 2 yards
Volume = Side length^3
Volume = 2^3
Volume = 8 cubic yards
Volume of the two cubes:
Since there are two cubes, the total volume of the cubes is 8 + 8 = 16 cubic yards.
Volume of the cuboid:
Length = 4.5 yards
Width = 2 yards (equal to the side length of cubes)
Height = 2 yards (equal to the side length of cubes)
Volume = Length x Width x Height
Volume = 4.5 x 2 x 2
Volume = 18 cubic yards
Total volume of the composite figure:
Volume = Volume of two cubes + Volume of the cuboid
Volume = 16 + 18
Volume = 34 cubic yards
Therefore, the volume of the composite figure is 34 cubic yards.
Volume of one cube:
Side length = 2 yards
Volume = Side length^3
Volume = 2^3
Volume = 8 cubic yards
Volume of the two cubes:
Since there are two cubes, the total volume of the cubes is 8 + 8 = 16 cubic yards.
Volume of the cuboid:
Length = 4.5 yards
Width = 2 yards (equal to the side length of cubes)
Height = 2 yards (equal to the side length of cubes)
Volume = Length x Width x Height
Volume = 4.5 x 2 x 2
Volume = 18 cubic yards
Total volume of the composite figure:
Volume = Volume of two cubes + Volume of the cuboid
Volume = 16 + 18
Volume = 34 cubic yards
Therefore, the volume of the composite figure is 34 cubic yards.
Use the image to answer the question.An illustration shows a hexagonal prism with the label Choosy Cheesy on the top surface. The height of the hexagonal prism is 8 centimeters. The two longer parallel sides of the hexagonal prism each measure 30 centimeters in length. One end of the prism is marked with a dashed line measuring 15 centimeters across, joining the two opposite vertices of the parallel edges, forming a triangular prism with a perpendicular measure of 8 centimeters. A sample of gourmet cheeses came in this box. What is the volume of the box?(1 point)
To find the volume of the box, we need to calculate the volume of the hexagonal prism and the volume of the triangular prism separately, and then add them together.
Volume of the hexagonal prism:
Base area of the hexagonal base = perimeter of base x apothem / 2
Perimeter of the base = 6 x side length = 6 x 30 cm = 180 cm
Apothem = height of the hexagonal prism = 8 cm
Base area = 180 x 8 / 2 = 90 x 8 = 720 cm²
Volume of the hexagonal prism = Base area x Height
Volume = 720 x 8 = 5760 cm³
Volume of the triangular prism:
Base area of the triangular base = 0.5 x base x height
Base area = 0.5 x 15 x 8 = 60 cm²
Volume of the triangular prism = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 5760 + 480 = 6240 cm³
Therefore, the volume of the box is 6240 cubic centimeters.
Volume of the hexagonal prism:
Base area of the hexagonal base = perimeter of base x apothem / 2
Perimeter of the base = 6 x side length = 6 x 30 cm = 180 cm
Apothem = height of the hexagonal prism = 8 cm
Base area = 180 x 8 / 2 = 90 x 8 = 720 cm²
Volume of the hexagonal prism = Base area x Height
Volume = 720 x 8 = 5760 cm³
Volume of the triangular prism:
Base area of the triangular base = 0.5 x base x height
Base area = 0.5 x 15 x 8 = 60 cm²
Volume of the triangular prism = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 5760 + 480 = 6240 cm³
Therefore, the volume of the box is 6240 cubic centimeters.
wrong
I apologize for the mistake. Let's reevaluate the calculation.
Volume of the hexagonal prism:
The hexagonal prism has a hexagonal base with side length = 30 cm, apothem (height) = 8 cm, and height of the prism = 8 cm.
The area of the hexagonal base = (1/2) x Perimeter of hexagon x apothem
Area = (1/2) x 6 x 30 x 8 = 720 cm²
Volume of the hexagonal prism = Base area x Height
Volume = 720 x 8 = 5760 cm³
Volume of the triangular prism:
The triangular prism has a base with base length = 15 cm, height = 8 cm, and length of the prism = 8 cm.
The area of the triangular base = (1/2) x Base x Height
Area = (1/2) x 15 x 8 = 60 cm²
Volume of the triangular prism = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 5760 + 480 = 6240 cm³
Therefore, the correct volume of the box is 6240 cubic centimeters.
Volume of the hexagonal prism:
The hexagonal prism has a hexagonal base with side length = 30 cm, apothem (height) = 8 cm, and height of the prism = 8 cm.
The area of the hexagonal base = (1/2) x Perimeter of hexagon x apothem
Area = (1/2) x 6 x 30 x 8 = 720 cm²
Volume of the hexagonal prism = Base area x Height
Volume = 720 x 8 = 5760 cm³
Volume of the triangular prism:
The triangular prism has a base with base length = 15 cm, height = 8 cm, and length of the prism = 8 cm.
The area of the triangular base = (1/2) x Base x Height
Area = (1/2) x 15 x 8 = 60 cm²
Volume of the triangular prism = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 5760 + 480 = 6240 cm³
Therefore, the correct volume of the box is 6240 cubic centimeters.
the answer is wrong
Apologies for the confusion. Let's correct it:
Volume of the hexagonal prism:
The area of the hexagonal base is given by the formula: Area = 3sqrt(3) x (side length)^2 / 2
Area = 3sqrt(3) x (30)^2 / 2 = 3sqrt(3) x 900 / 2 = 1350sqrt(3) cm²
Now, we can find the volume of the hexagonal prism:
Volume = Base area x Height
Volume = 1350sqrt(3) x 8 = 10800sqrt(3) cm³
Volume of the triangular prism:
The area of the triangular base is given by the formula: Area = (base length x height) / 2
Area = (15 x 8) / 2 = 60 cm²
Now, we can find the volume of the triangular prism:
Volume = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 10800sqrt(3) + 480 ≈ 11845.4 cubic centimeters
Therefore, the volume of the box is approximately 11845.4 cubic centimeters.
Volume of the hexagonal prism:
The area of the hexagonal base is given by the formula: Area = 3sqrt(3) x (side length)^2 / 2
Area = 3sqrt(3) x (30)^2 / 2 = 3sqrt(3) x 900 / 2 = 1350sqrt(3) cm²
Now, we can find the volume of the hexagonal prism:
Volume = Base area x Height
Volume = 1350sqrt(3) x 8 = 10800sqrt(3) cm³
Volume of the triangular prism:
The area of the triangular base is given by the formula: Area = (base length x height) / 2
Area = (15 x 8) / 2 = 60 cm²
Now, we can find the volume of the triangular prism:
Volume = Base area x Height
Volume = 60 x 8 = 480 cm³
Total volume of the box:
Volume = Volume of hexagonal prism + Volume of triangular prism
Volume = 10800sqrt(3) + 480 ≈ 11845.4 cubic centimeters
Therefore, the volume of the box is approximately 11845.4 cubic centimeters.
3 answers