Question

A solid square pyramid has a mass of 750 g. It is made of a material with a
density of 8.05 g/cm'. Given that the height of the pyramid is 13.5 cm, find the
length of its square base.​

Answer 1

Answer:

4.55cm

Step-by-step explanation:

The unit of a volume: $cm^3$

The unit of a density: $\dfrac{g}{cm^3}$

The density is $\dfrac{mass}{volume}$

Substitute:

$\dfrac{8.05g}{cm^3}=\dfrac{750g}{V}$

cross multiply

$8.05gV=750gcm^3$

divide both sides by 8.05g

$V\approx93.17cm^3$

The formula of a volume of a square pyramid:

$V=\dfrac{1}{3}a^2H$

a - length of  square base

H - height of a pyramid

We have:

$V=93.17cm^3;\ H=13.5cm$

Substitute:

$93.17=\dfrac{1}{3}a^2(13.5)$

multiply both sides by 3

$279.51=13.5H$

$297.51=13.5a^2$

divide both sides by 13.5

$a^2\approx20.7\to a=\sqrt{20.7}\approx4.55(cm)$

Answer 2

Answer:

Step-by-step explanation:

volume of pyramid=1/3×base area×height

let the length of base=x

base area=x²

volume V=1/3×x²×13.5=4.5 x²

mass=volume×density

750=4.5 x²×8.05=36.225 x²

x²=750/36.225

x=√(750/36.225)≈4.55 cm