Question

The weight of a solid cone having diameter $14$ cm and vertical height $51$ cm is ____ if the material of solid cone weighs $10$ grams per cubic cm.

• A. $26.18$ kg
• B. $2.18$ kg
• C. $6.18$ kg
• D. None of these

Answer 1

The correct option is A $26.18$ kg

Given, diameter $d=14cm$.

Let $r$ be the radius of the cone.

$r=\frac{d}{2}=\frac{14}{2}=7$.

Also, height $h=51cm$.

Therefore, Volume of cone $=\frac{\pi }{3}{r}^{2}h$.

$\Rightarrow V=\frac{\pi }{3}\times 7^2\times 51=\frac{22}{7}\times 49\times 51\times \frac{1}{3}=2618c{m}^3$.

As weight of $1c{m}^3=10gm$,

$\Rightarrow$weight of $2618c{m}^3=26180gm$

$\Rightarrow 26.18kg$.

Hence, option $A$ is correct.