Question

The ratio between the base edges of two square pyramids is 1:4. If the heights are also in the same ratio and the volume of the second pyramid is 400 cubic centimetres, what is the volume of the first square pyramid?

• A. $20cubiccentimetres$
• B. $16cubiccentimetres$
• C. $6.25cubiccentimetres$
• D. $4cubiccentimetres$

Answer 1

The correct option is C

$6.25cubiccentimetres$

Let $v_1$ and Let $v_2$ denote the volume of the first and the second square pyramid respectively. Now, if $a_1$, $a_2$ represent the lengths of the base edges and $h_1$, $h_2$ represent the heights of the first and the second square pyramids respectively, then we have $\frac{a_1}{a_2}=\frac{1}{4}$ and
$\frac{h_1}{h_2}=\frac{1}{4}$ and $v_2=400cubiccentimetres$
Also, $\frac{v_1}{v_2}=\frac{\frac{1}{3}\times a_1^2\times h_1}{\frac{1}{3}\times a_2^2\times h_2}$
$⟹\frac{v_1}{v_2}=(\frac{a_1}{a_2}{)}^2\times \frac{h_1}{h_2}$

$⟹\frac{v_1}{400}=(\frac{1}{4}{)}^2\times \frac{1}{4}$
$⟹\frac{v_1}{400}=\frac{1}{64}$
$⟹v_1=\frac{400}{64}=6.25cubiccentimetres$