Objects and Solids

A sphere is a three-dimensional shape where every point on its surface is ​ (a)   from its center. When you slice a sphere with a plane, the cross section is always a ​ (b)   . Interestingly, a cone can also have a circular cross section. A cone is a three-dimensional shape with a ​ (c)   that tapers smoothly to a point called the apex. If you slice a cone ​ (d)   , the cross section is a circle. Therefore, both a sphere and a cone can have circular cross sections, making them similar in this aspect.

• equidistant

• circle

• circular base

• parallel to its base

• 1) rectangular prism

• 2) cone

• 3) square pyramid

• 4) pyramid frustum

• F
• G
• H
• I

Two similar cones have a scale factor of 8/27. What is the ratio of their volumes?

• 2/3

• 64/729

• 512/19683

• 8/27

What is the scale factor of the side lengths of the figure on the left to the figure on the right.

• 3/1

• 3240/120

• 27/1

• 9/1

The surface area of a certain prism is 1088 square km and its volume is 13312 cubic km. If a similar solid has a surface area of 425 square km, what is this similar solids volume?

• 3250 cubic km

• 5200 cubic km

• 1950 cubic km

• 8320 cubic km

Two similar cylinders have surface areas of 40π ft² and 90π ft². What is the ratio of the height of the large cylinder to the height of the small cylinder?

• 4/9

• 2/3

• 8/27

• 16/81

What 3-D solid is formed when this rectangle is rotated about the vertical line?

• Right, rectangular prism

• Right, circular cylinder

• Right, oval cylinder

• Right, square prism

What is the exact volume of the pyramid?

• 48 cm³

• 144 cm³

• 288 cm³

• 96 cm³

Find the volume.

• 1,444.48 ft³

• 1,745.92 ft³

• 2,132.08 ft³

• 2,951.68 ft³