Question

Find the volume of the pyramid. The height is 7.2 inches and the slant height is 9.7 inches.

Answer 1

hello

i'll try to draw an image of the pyramid first

assuming the pyramid have a square base, we need to find the lengthof each side before we can find the volume of the pyramid

to find the value of x, we can assume a right angle triangle and use pythagora's theorem to solve for x

`\begin{gathered} x^2=y^2+z^2 \\ 9.7^2=y^2+7.2^2 \\ 94.09=y^2+51.84 \\ y^2=94.09-51.84 \\ y^2=42.25 \\ \text{take the square root of both sides} \\ √(y^2)=√(42.25) \\ y=6.5 \end{gathered}`

the length of the square is to 2y since the base of the triangle = 2y

the volume of a pyramid can thus be calculated by 1/3LSH

L= length of base

S= slant height

H= height

`\begin{gathered} \text{vol. of a pyramid }=(1)/(3)* L* S* H \\ \text{vol. of a pyramid}=(1)/(3)*13*7.2*9.7 \\ \text{vol. }=(1)/(3)*907.92 \\ \text{volume of the pyramid = 302.64} \end{gathered}`

the volume of the given pyramid is 302.64 inches