1.
Given a right circular cone.

a) What is the shape of a cross section parallel to the base of the cone?
Choose:
 triangle rectangle circle oval

b)
What is the shape of a cross section perpendicular to the base of the cone?
Choose:
 triangle rectangle circle oval

2.
A right square pyramid sits atop a right circular cylinder as shown at the right. A sword will make a vertical slice through both figures starting at the vertex of the pyramid. Which of the following shapes represents the cross section?
Choose:

3.
The area of the base of a cone is 24 sq. cm. and its height is 16 cm. What is the area of a cross section parallel to the base and 4 cm. from the vertex?

Choose:
 4 cu. cm. 6 cu. cm. 1½ cu. cm. 4½ cu. cm.

4.
A hot water pipeline in Iceland is composed of sections of right circular cylinder pipe. When the pipe is cut perpendicular to its base, the cross section has a diameter of 90 cm.
a) What is the area of the cross section, to the nearest tenth of a square centimeter?
Choose:
 282.7 3854.3 25446.9 6361.7

Note

1 square meter = 10,000 square centimeters

b) How many cubic meters of water can be contained in 35 meters of pipe?
Choose:
 24.5 cu. m. 223 cu. m. 22.3 cu. m. 2230 cu. m.

5.
Given a right circular cylinder with a radius of 8 inches and a height of 20 inches. Which of the following choices is NOT a possible cross section of this cylinder?
Choose:
 circle oval square rectangle

6.
A right circular cylinder has a height of 30 units and a radius of 5 units.
a) Find the area of a cross section parallel to the base. Express answer to the nearest tenth of a square unit.
Choose:
 31.4 square units 78.5 square units 235.6 square units 742.5 square units

b) Find the area of a cross section through the center of the cylinder, perpendicular to the base.
Choose:
 150 square units 2355 square units 300 square units 1500 square units

7.
A right circular cylinder is cut out of a right rectangular prism. The prism measures 6 in. by 5 inches by 15 inches. The radius of the cylinder is 2 inches. If the remaining solid is sliced parallel to its base,
a) what is the area of that cross section, to the nearest tenth of a square inch?
Choose:
 17.4 sq. in. 12.6 sq. in. 42.6 sq. in. 16.5 sq. in.

b)
what is the volume of the structure after the cut out, to the nearest tenth of a cubic inch?
Choose:
 450.0 cubic inches 188.5 cubic inches 638.5 cubic inches 261.5 cubic inches

8.
A plane intersects a sphere. (The plane is not tangent to the sphere.) Which of the following statements is true regarding the cross section formed by the plane?
Choose:
 The cross section is always a circle. The cross section is sometimes a circle. The cross section is always an oval. The cross section is sometimes a square.

9.
A hemisphere of radius 3.5 cm. is sliced vertically through its center.
What is the area of the cross section obtained by the slice, to the nearest tenth of a centimeter?
Choose:
 5.5 9.6 19.2 11

10.
A sphere has a radius of 5 units. The sphere is sliced 3 units below its center. What is the area of the cross section obtained from this slice, to the nearest tenth of a square unit?

Choose:
 12.6 sq. units 402.1 sq. units 50.3 sq. units 804.2 sq. units