Question

A square shaped pyramid container is shown below in the figure.

If each side of its square(a) is reduced by 30% and its height(h) is increased by 30%, find the change in volume of the container.

• A. -15.12%
• B. +36.3%
• C. +15.12%
• D. -36.3%

Answer 1

The correct option is D -36.3%

For the given figure,

$\text{Volume of container}=\frac{1}{3}\times \text{area of base}\times \text{height}$

$\text{Area of base =}{a}^2$
$\therefore \text{Volume of container(V)}=\frac{1}{3}\times a^2\times h$

Since each side decreases by 30%,
New side length = 0.7a
Similarly,
Since height increases by 30%,
New height = 1.3h

$\text{New volume of the container (V1) =}\frac{1}{3}\times (0.7a{)}^2\times 1.3h$
$=0.637V$

$\text{Change in \% of volume =}\frac{\text{New volume of the container - Initial volume}}{\text{Initial Volume}}\times 100$

$=\frac{\text{0.637 V - V}}{\text{V}}\times 100$
$=-36.3\%$
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