Question

question 11
cl. 2 test review - algebra 1
the volume of a right pyramid is given by the formula ( v=\frac{1}{3}bh ), where ( b ) is the area of the base and ( h ) is the height
solve the formula for ( h ). then find the height, in inches, of a right pyramid with a volume of 100 cubic inches and a base area of 225 square inches.
a) ( h=\frac{v}{b} ) 12 inches
b) ( h=\frac{v}{b} ) 0.08 inches
c) ( h=\frac{3v}{b} ) 4 inches
d) ( h = v-\frac{1}{3}b ) 925 inches

Explanation:

Step1: Solve the formula for \( h \)

Given \( V=\frac{1}{3}Bh \). Multiply both sides by \( 3 \) to get \( 3V = Bh \). Then divide both sides by \( B \): \( h=\frac{3V}{B} \).

Step2: Substitute \( V = 100 \) and \( B = 25 \)

Substitute \( V = 100 \) and \( B = 25 \) into \( h=\frac{3V}{B} \). So \( h=\frac{3\times100}{25} \).
Calculate \( 3\times100 = 300 \), then \( \frac{300}{25}=12 \).

Answer:

A. \( h=\frac{3V}{B}, 12\) inches