Question

A triangular prism has a base of an equilateral triangle of side 3.5 cm. Water is filled till the height of 10 cm in the prism. If a small ice cube of side 2 cm is put inside it, the water level rises to different height. What is the new height?

• A. 12.5 cm
• B. 13.5 cm
• C. 11.5 cm
• D. 10.5 cm

Answer 1

The correct option is C 11.5 cm

Side of the equilateral triangle = 3.5 cm

Area of the base = $\frac{\sqrt{3}}{4}\times (3.5{)}^2$

Let the height of water displaced in the prism = h cm.

Volume of solid cube = Volume of water displaced in the prism

$\Rightarrow 2\times 2\times 2$ = $\frac{\sqrt{3}}{4}\times (3.5{)}^2\times h$

$\Rightarrow h=\frac{2\times 2\times 2\times 4}{\sqrt{3}\times 3.5\times 3.5}$

$\Rightarrow h=1.5cm$

Since the water level rises by 1.5 cm, the new heieght = $10+1.5=11.5cm$

So, new height is 11.5 cm.