×

# SAT Solid Geometry

When placed inside a cube, a sphere is tangent to all the faces of the cube. If the surface area of the cube is $$150$$ cm$$^2,$$ what is the radius of the sphere in centimeters?

(A) $$\ \ 2.5$$
(B) $$\ \ 5$$
(C) $$\ \ 10$$
(D) $$\ \ 25$$
(E) $$\ \ 75$$



A plastic tube is $$10$$ cm long. If the inside of the tube is empty, its inner radius is $$r=7$$ cm and its outer radius is $$R=9$$ cm, what is the volume of plastic used to create the tube, in cubic centimeters?

(A) $$\ \ 32\pi$$
(B) $$\ \ 320\pi$$
(C) $$\ \ 490 \pi$$
(D) $$\ \ 810\pi$$
(E) $$\ \ 1300\pi$$



A regular hexagonal pyramid has height $$h=6,$$ and base edges $$b = 10.$$ What is the volume of the pyramid? (The volume of a pyramid can be found using the formula $$V = \frac{1}{3}Bh,$$ where $$B$$ is the area of the base.)

(A) $$\ \ 50\sqrt{3}$$
(B) $$\ \ 150\sqrt{3}$$
(C) $$\ \ 300$$
(D) $$\ \ 300\sqrt{2}$$
(E) $$\ \ 300\sqrt{3}$$



Shown above is a model of a staircase that is to be made of concrete. If each step has the shape of a rectangular solid, and $$s=2$$ in, how many cubic inches of concrete will be needed to create the stairs?

(A) $$\ \ 8$$
(B) $$\ \ 24$$
(C) $$\ \ 40$$
(D) $$\ \ 80$$
(E) $$\ \ 120$$

A cylinder and a sphere have the same radius, $$r=27.$$ If the volume of the sphere is twice bigger than that of the cylinder, what is the height of the cylinder? (The volume of a sphere can be found using the formula $$V = \frac{4}{3}\pi r^3.$$)

(A) $$\ \ 13.5$$
(B) $$\ \ 18$$
(C) $$\ \ 36$$
(D) $$\ \ 72$$
(E) $$\ \ 486$$

×