Similarity with Area and Volume

Farmer Fred has a silo that looks like the one in the picture. The cylinder part is 20 feet tall with a radius of 6 feet. What is the volume of the entire silo? Round to the nearest whole number.

• 3167 ft³

• 2337 ft³

• 2413 ft³

• 2714 ft³

Two similar rectangular prisms have a surface area of 240 square meters and 735 square meters. If the volume of the larger prism is 10290 cubic meters, what is the volume of the smaller prism?

Mathematical Equivalence

ON

Two spheres have a scale factor ratio of 1:3.  The smaller sphere has a surface area of 16 ft²_.  Find the surface area of the larger sphere.

• 48 ft²

• 144 ft²

• 432 ft²

• 32 ft²

Find the volume of this sphere.

• 150.72 mm³

• 904.32 mm³

• 2,712.96 mm³

• 452.16 mm³

The volume of drink A is 27 oz. The volume of drink B is 64 oz. The surface area of drink A is 270 in². What is the surface area of drink B?

• 480 in²

• 640 in²

• 360 in²

• 203 in²

How many times larger is the the volume of a cylinder if the radius is doubled?

• 2 times larger

• 4 times larger

• 8 times larger

• 16 times larger

The two figures are similar. Find the scale factor of the figure on the left to the figure on the right. Then find the ratio of surface areas and the ratio of volumes.

• 2:9, 4:81, 8:729

• 2:9, 4:9, 4:81

• 2:9, 4:81, 14:6561

• 2:9, 8:729, 4:81

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

Determine whether each pair of solids is similar, congruent or neither. If the solids are similar, state the scale factor( use column :)

Determine whether each pair of solids is similar, congruent or neither. If the solids are similar, state the scale factor