Solid Geometry

Practice Questions

ISEE Upper Level (grades 9-12) Quantitative Reasoning › Solid Geometry

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1

In terms of , give the surface area, in square inches, of a spherical water tank with a diameter of 20 feet.

2

In terms of , give the volume, in cubic feet, of a spherical tank with diameter 36 inches.

3

In terms of , give the surface area, in square inches, of a spherical water tank with a diameter of 20 feet.

4

is a positive number. Which is the greater quantity?

(A) The surface area of a sphere with radius

(B) The surface area of a cube with edges of length

5

In terms of , give the surface area, in square inches, of a spherical water tank with a diameter of 20 feet.

6

is a positive number. Which is the greater quantity?

(A) The volume of a cube with edges of length

(B) The volume of a sphere with radius

7

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

8

What is the surface area of a cylinder of height in, with a radius of in?

9

Pyramid 1 has a square base with sidelength ; its height is .

Pyramid 2 has a square base with sidelength ; its height is .

Which is the greater quantity?

(a) The volume of Pyramid 1

(b) The volume of Pyramid 2

10

What is the surface area of a cylinder of height in, with a radius of in?

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