Question

the volume of the rectangular pyramid is 360 cubic feet. the height, h, is 15 feet, and the width of the base, w, is 6 feet. what is the length of the base, l, of the rectangular pyramid? (not drawn to scale) a 12 ft b 13 ft c 36 ft d 90 ft right rectangular prism s.a. = 2(lw + wh + hl) right prism s.a. = ph + 2b right cylinder s.a. = 2πr² + 2πrh right cone s.a. = πrl + πr² regular pyramid s.a. = (pl)/2 + b sphere s.a. = 4πr² cylinder v = πr²h cone v = (1/3)πr²h pyramid v = (1/3)bh sphere v = (4/3)πr³

Explanation:

Step1: Recall pyramid volume formula

Volume of pyramid: $V = \frac{1}{3}Bh$, where $B$ is base area.

Step2: Substitute base area expression

Base is rectangle: $B = l \times w$. So $V = \frac{1}{3}(l \times w)h$.

Step3: Plug in known values

$360 = \frac{1}{3}(l \times 6) \times 15$. Simplify: $360 = (l \times 6) \times 5$.

Step4: Solve for $l$

$360 = 30l \implies l = \frac{360}{30} = 12$.

Answer:

A. 12 ft