Question

A rectangular pyramid has a height of $15$ ft and a volume of $405$ cu ft. Which of the following options is not a possibility for the given pyramid?

• A. The length and width of the base are $16.2$ ft and $5$ ft
• B. If the width of the base is $5.4$, then the length is the same as its height
• C. The width and length of the base are $9$ ft and $27$ ft
• D. The base area of the pyramid is $81$ sq ft

Answer 1

The correct option is C The width and length of the base are $9$ ft and $27$ ft

Volume of the rectangular pyramid $=\frac{1}{3}$ Base area $\times$ Height

$\therefore \frac{1}{3}$ Base area $\times$ Height $=405$

$\frac{1}{3}$ Base area $\times 15=405$

Base area $=\frac{405\times 3}{15}=81$

The base area of the pyramid is $81$ sq ft.

Thus, option A is true.

Option B
Length $=16.2$ ft, Width $=5$ ft
Base area
$=16.2\times 5=81$
Thus, option B is true.

Option C
Length $=27$ ft, Width $=9$ ft
Base area $=27\times 9=243\ne 81$
Thus, option C is not true.

Option D
Length $=15$ ft, Width $=5.4$ ft
Base area $=15\times 5.4=81$
Thus, option D is true.