Volume and Cross Sections: 8th Grade Math Challenge

A cylindrical water tank has a radius of 3 feet and a height of 10 feet. What is the volume of the tank? If the tank is cut in half horizontally, what is the volume of each half?

• 60π cubic feet for the full tank, 30π cubic feet for each half

• 100π cubic feet for the full tank, 50π cubic feet for each half

• 90π cubic feet for the full tank, 45π cubic feet for each half

• 75π cubic feet for the full tank, 37.5π cubic feet for each half

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A rectangular prism has a length of 4 meters, a width of 3 meters, and a height of 5 meters. If you slice the prism vertically through the length, what is the area of the cross section created?

• 12 square meters

• 15 square meters

• 20 square meters

• 10 square meters

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A cone has a base radius of 2 inches and a height of 6 inches. Calculate the volume of the cone. If you slice the cone horizontally at a height of 2 inches, what is the volume of the smaller cone formed?

• 4π cubic inches for the original cone and 1.5π cubic inches for the smaller cone.

• 6π cubic inches for the original cone and 1.5π cubic inches for the smaller cone.

• 8π cubic inches for the original cone and 2.3625π cubic inches for the smaller cone.

• 10π cubic inches for the original cone and 3.14π cubic inches for the smaller cone.

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A triangular prism has a base area of 12 square centimeters and a height of 8 centimeters. What is the volume of the prism? If you cut the prism parallel to the base, what will be the area of the cross section?

• Volume: 96 cm³, Cross section area: 12 cm²

• Volume: 100 cm³, Cross section area: 12 cm²

• Volume: 72 cm³, Cross section area: 10 cm²

• Volume: 80 cm³, Cross section area: 15 cm²

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A sphere has a radius of 5 cm. What is the volume of the sphere? If you slice the sphere through its center, what is the area of the circular cross section?

• Volume: 250π cm³, Area of cross section: 20π cm²

• Volume: (500/3)π cm³, Area of cross section: 25π cm²

• Volume: 100π cm³, Area of cross section: 30π cm²

• Volume: (300/3)π cm³, Area of cross section: 15π cm²

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A rectangular pool is 10 meters long, 4 meters wide, and 2 meters deep. What is the volume of the pool? If you take a cross section of the pool at a depth of 1 meter, what is the area of that cross section?

• Volume: 80 cubic meters; Cross section area: 50 square meters

• Volume: 60 cubic meters; Cross section area: 30 square meters

• Volume: 80 cubic meters; Cross section area: 40 square meters

• Volume: 100 cubic meters; Cross section area: 20 square meters

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A cylinder has a height of 12 cm and a diameter of 6 cm. Calculate the volume of the cylinder. If you make a horizontal cut at 4 cm from the base, what is the volume of the top section?

• 36π cm³

• 48π cm³

• 60π cm³

• 72π cm³

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A square pyramid has a base side length of 6 cm and a height of 9 cm. What is the volume of the pyramid? If you slice the pyramid parallel to the base at a height of 3 cm, what is the area of the cross section?

• Volume: 108 cm³, Cross section area: 4 cm²

• Volume: 72 cm³, Cross section area: 6 cm²

• Volume: 54 cm³, Cross section area: 9 cm²

• Volume: 120 cm³, Cross section area: 2 cm²

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A rectangular box has dimensions of 8 cm by 5 cm by 3 cm. What is the volume of the box? If you cut the box in half along the width, what is the volume of each half?

• The volume of the box is 120 cm³; the volume of each half is 60 cm³.

• The volume of the box is 120 cm³; the volume of each half is 40 cm³.

• The volume of the box is 150 cm³; the volume of each half is 75 cm³.

• The volume of the box is 100 cm³; the volume of each half is 50 cm³.

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A right circular cone has a base radius of 4 inches and a height of 9 inches. Calculate the volume of the cone. If you slice the cone horizontally at a height of 3 inches, what is the volume of the smaller cone formed?

• 64π cubic inches for the original cone, 24π cubic inches for the smaller cone.

• 32π cubic inches for the original cone, 8π cubic inches for the smaller cone.

• 48π cubic inches for the original cone, 16π/9 cubic inches for the smaller cone.

• 48π cubic inches for the original cone, 12π cubic inches for the smaller cone.

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