A right square pyramid has a height of 9\text{ centimeters} and a square base with a side … — SAT

A right square pyramid has a height of $9\text{ centimeters}$ and a square base with a side length of $5\text{ centimeters}$ . What is the volume, in cubic centimeters, of the pyramid?

A
15
B
45
75Answer
D
225

Answer

The volume of a right square pyramid is given by the formula

V = \frac{1}{3}Bh

, where

B

is the area of the base and

h

is the height. Since the base is a square with side length

5\text{ centimeters}

, its area is

B = 5^2 = 25\text{ square centimeters}

. Substituting the base area and the height of

9\text{ centimeters}

into the formula gives

V = \frac{1}{3} \times 25 \times 9 = 75\text{ cubic centimeters}

Step-by-Step Solution

Calculate the area of the square base (

B

B = 5^2 = 25\text{ square centimeters}

The base is a square with side length

5\text{ centimeters}

, and the area of a square is calculated by squaring its side length.

Apply the volume formula for a pyramid:

V = \frac{1}{3}Bh

V = \frac{1}{3} \times 25 \times 9 = 75\text{ cubic centimeters}

Substituting the base area of

25\text{ square centimeters}

and the height of

9\text{ centimeters}

into the pyramid volume formula yields the volume.

Key Concept

The volume of a pyramid is calculated using the formula

V = \frac{1}{3}Bh

, where

B

is the area of the base and

h

is the height.

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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