Question

Find the volume of a cone of radius 10cm and slant height 18cm.

Answer 1

$\huge\text{\underline{Answer}}$

$\sf{\underline{Given }}$

Radius = 10 cm

Slant height = 18 cm

$\sf{\underline{To find }}$

Volume of cone = ?

$\huge\sf{solution:}$

Volume of cone =

$\boxed{\sf{ \frac{1}{3} \pi {r}^{2} h}}$

where h is height of cone.

Now we have to find height of cone.

Height of cone = $\bold{\sqrt{ {l}^{2} - {r}^{2} } }$

put the value of r and l.

$\implies$ $\bold{h =\sqrt{ {18}^{2} - {10}^{2} } }$

$\implies$ $\bold{h = \sqrt{324 - 100 }}$

$\implies$ $\bold{h =\sqrt{224} }$

$\implies$ $\bold{h =4 \sqrt{14} cm }$

Now volume of cone = $\bold{ \frac{1}{3} \pi {r}^{2} h}$

$\implies$ $\bold{V = \frac{1}{3} \times \frac{314}{100} \times {10}^{2} \times 4 \sqrt{14} }$

$\implies$ $\bold{V = \frac{1}{3} \times \frac{314}{100} \times 100 \times 4 \sqrt{14} }$

$\implies$ $\bold{V= \frac{314}{3} \times 4 \sqrt{14} }$

$\implies$ $\bold{V =\frac{4699.52}{3} }$

$\implies$ $\bold{V =1566.50}$

hence,volume of cone = 1566.50 cm ^3.

Answer 2

Answer:

$volume \ of \ cone=1567.3 \ cm^{3}$

Step-by-step explanation

$we \ have \ l=18cm \ and \ r=10cm\\\\Let's \ find \ height \ by \ formula\\\\l^{2}=h^{2}+r^{2}\\\\putting \ value \ of \ l \ and \ r \ here\\\\h^{2}= 18^{2}-10^{2}\\ \\h=\sqrt{324-100}\\\\ h=4\sqrt{14} \ cm \\\\\ we \ know \ formula \ of \ volume \ of \ cone\\\\volume \ of \ cone=\frac{1}{3}\pi r^{2}h\\ \\putting \ value \ of \ l,r \ and \ h \ here\\\\volume \ of \ cone=\frac{1}{3}*3.14*10^{2}*4\sqrt{14} \ cm^{3}\\\\volume \ of \ cone=314*2*2.44 \ cm^{3}\\\\volume \ of \ cone=1567.3 \ cm^{3}$