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=(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=(1)/(3) B*h\\ \\ h=(3*V)/(B) \\ \\ h=(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) +(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) +(6)/(2) ^(2)`

`l^(2) =4^(2) +3^(2)`

`l =5\ in`

therefore

the answer is the option

C. 5 inches