Question

The base of a prism is a right triangle with the sides perpendicular to each other of lengths 5 cm and 10 cm respectively. If the height of the prism is 100 cm, then the amount of water it will displace when placed in a container filled with water will be _____.

• A. 1500 $c{m}^3$
• B. 2000 $c{m}^3$
• C. 2550 $c{m}^3$
• D. 2500 $c{m}^3$

Answer 1

The correct option is D 2500 $c{m}^3$

Here, volume of water displaced = volume of the prism

Since, the triangle is a right-angled triangle,

Area = $\frac{1}{2}\times \text{base}\times \text{height}$

= $\frac{1}{2}\times 5\times 10=25c{m}^2$

Now, volume of the prism = base area $\times$ height

$=25\times 100$ (since height is given as 100 cm)

$=2500c{m}^3$

So, the volume of water displaced is 2500 $c{m}^3.$