Question

Helen has 48 cubic inches of clay to make a solid right pyramid with a base edge measuring 6 inches. Which is the slant height of the pyramid if Helen uses all the clay?

A. 3 inches
B. 4 inches
C. 5 inches
D. 6 inches

Answer 1

The answer is C. 5 inches

Answer 2

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3} B*h$

where B is the area of the base

h is the height of the pyramid

Step $1$

Find the height of the pyramid

we know that

the base is a square

so

$B=6^{2} =36\ in^{2}$

$V=48\ in^{3}$

$V=\frac{1}{3} B*h\\ \\ h=\frac{3*V}{B} \\ \\ h=\frac{3*48}{36} \\ \\ h=4\ in$

Step $2$

Find the slant height of the pyramid

we know that

Applying the Pythagorean Theorem

$l^{2} =h^{2} +\frac{b}{2} ^{2}$

where

l is the slant height

h is the height of the pyramid

b is a base edge of the pyramid

Substitute

$l^{2} =4^{2} +\frac{6}{2} ^{2}$

$l^{2} =4^{2} +3^{2}$

$l =5\ in$

therefore

the answer is the option

C. 5 inches