# ISEE Upper Level Quantitative : How to find the surface area of a sphere

## Example Questions

### Example Question #1 : How To Find The Surface Area Of A Sphere

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

Explanation:

feet =  inches, the diameter of the tank; half of this, or 120 inches, is the radius. Set , substitute in the surface area formula, and solve for :

### Example Question #5 : Spheres

Which is the greater quantity?

(a) The surface area of a sphere with radius 1

(b) 12

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

(a) is greater.

Explanation:

The surface area of a sphere can be found using the formula

.

The surface area of the given sphere can be found by substituting :

so , or

This makes (a) greater.

### Example Question #341 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Sphere A has volume . Sphere B has surface area . Which is the greater quantity?

(a) The radius of Sphere A

(b) The radius of Sphere B

(a) is greater

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

(b) is greater

Explanation:

(a) Substitute  in the formula for the volume of a sphere:

inches

(b) Substitute  in the formula for the surface area of a sphere:

inches

(b) is greater.

### Example Question #1 : How To Find The Surface Area Of A Sphere

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

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater