A cube with edges of length \$14\sqrt3\$ is inscribed in a sphere with a volume of qπ. What is the value of q?

A) 12348

B) 12438

C) 13248

D) 12384

The volume of a cube is 640 cubic units. What is the ratio of the volume of this cube to the volume of a cube whose surface area is 480 square units?

A) \$2 : 5\$

B) \$2 : \sqrt5\$

C) \$\sqrt5 : 2\$

D) \$4 : \sqrt5\$

The volume of the pyramid shown in the figure can be represented by the function \$V(x) = x^3 + x^2\$, which of the following expressions represents the pyramid’s height?

A) \$1/5\$

B) \$1/3\$

C) \$1/2\$

D) \$1/7\$

Containers A and B are in the shape of a right circular cylinder and have the same volume. If the radius of the base of Container A is 6 times the length of the radius of the base of Container B, what is the ratio of the height of Container A to the height of Container B?

A) 1 : 18

B) 1 : 12

C) 1 : 6

D) 1 : 36

Calculate the height of the given triangular prism with a volume of \$450\$ \$cm^3\$.

A) 6.5 cm

B) 8.5 cm

C) 5.7 cm

D) 7.5 cm

Find the area of the base of a square pyramid if its volume is \$1372\$ \$cm^3\$ and height is 21 cm.

A) 186 sq.cm

B) 14 sq.cm

C) 196 sq.cm

D) 176 sq.cm

If the volume of a sphere is tripled, by what factor does its radius increase?

A) ∛4

B) ∛3

C) ∛5

D) ∛6

What is the volume of a sphere whose radius is equal to the side length of a square with an area of \$225\$ \$cm^2\$?

A) \$14130\$ \$cm^3\$

B) \$11430\$ \$cm^3\$

C) \$14310\$ \$cm^3\$

D) \$14103\$ \$cm^3\$

What is the volume of a rectangular pyramid if the length and width of the rectangular base are 10 cm and 8 cm, respectively, and the pyramid’s height is 16 cm?

A) \$462.6 cm^3\$

B) \$426.6 cm^3\$

C) \$456.6 cm^3\$

D) \$466.6 cm^3\$

If a cone two-sixth the height of a large cone was sliced off the top of the large cone, what fraction of the large cone’s volume remained?

A) \$27/26\$

B) \$26/29\$

C) \$26/27\$

D) \$27/25\$