Question

Each side of the base of a square pyramid is reduced by $20$. By what percent must the height be increased so that the volume of the new pyramid is the same as the volume of the original pyramid?

• A. 20
• B. 40
• C. 46.875
• D. 56.25
• E. 71.875

Answer 1

Answer: (D)

56.25

Let $a$ be the side of the square.

Length of side of square when reduced by $20\%=a-\frac{20a}{100}=0.8a$

Let $a_1=0.8a$

Volume of pyramid $V=\frac{1}{3}\times$ Area of base $\times height=\frac{1}{3}A\times h$

Area of base with side $a=a^2$

$a^2=0.8a$

$V_1=\frac{1}{3}\times {\left(a_1\right)}^2\times h_1$

$V_1=V$ ....... [Given]

$\Rightarrow \frac{1}{3}{a}^2\times h=\frac{1}{3}{\left(0.8\right)}^2{a}^2\times h_1$

$\therefore h_1=1.5625h$

$⟹\frac{h_1-h}{h}=1.5625-1=56.25$

$\therefore$ 'h' need to be increase by $56.25$