Question

question 1 (multiple choice worth 1 points)
(volume lc)
the base of a rectangular pyramid measures 14 inches by 7 inches. the height of the pyramid is 11.5 inches. what is the volume of the pyramid?
483 in³
1,127 in³
161 in³
375.67 in³

Explanation:

Step1: Calculate the base area

The base is a rectangle with length \( l = 14 \) inches and width \( w = 7 \) inches. The area of a rectangle is \( A=l\times w \). So, \( A = 14\times7=98\) square inches.

Step2: Use the volume formula for a pyramid

The volume formula for a pyramid is \( V=\frac{1}{3}Ah\), where \( A \) is the base area and \( h \) is the height. Here, \( A = 98\) square inches and \( h=11.5\) inches. Then \( V=\frac{1}{3}\times98\times11.5\).
First, calculate \( 98\times11.5 = 1127\). Then \( V=\frac{1127}{3}\approx375.67\) cubic inches.

Answer:

\(375.67\space in^{3}\) (the fourth option)