Question

The base radius of a cone is 15 cm and its slant height is 25 cm find the volume

Answer 1

Explanation:-

We have :-

✧ Base radius of cone (r) = 15cm

✧ Slant height (l) = 25 cm

Required to find :-

Volume of cone

SoLuTiOn :-

$\: \: \: \bullet \boxed{ \underline{ \pmb{volume \: of \: cone = \frac{1}{3} \pi \: r {}^{2}h }}}$

where,

r = radius of cone

h = height of cone.

But we don't know the height of cone. So, By using relation between radius, height, slant height of cone

We can find the height of cone.

$\: \: \bullet \: \boxed{ \underline{ \pmb{l = \sqrt{r {}^{2} + h {}^{2} } }}}$

where,

l = slant height

r = radius

h = height

$\implies \: \sf \: 25= \sqrt{(15) {}^{2} + h {}^{2} }$

$\: \: \: \: \: \: \: \implies \: \sf \: (25) {}^{2} = (15) {}^{2} + h {}^{2}$

$\: \: \: \: \: \: \: \implies \: \sf \: 625 = 225 + h {}^{2}$

$\: \: \: \: \: \: \: \implies \: \sf \: 625 - 225 = h {}^{2}$

$\: \: \: \: \: \: \: \: \: \: \implies \: \sf \: 400 = h {}^{2}$

$\: \: \: \: \: \implies \: \sf \: (20) {}^{2} = h {}^{2}$

$\boxed{ \bf \: h = 20cm}$

Now, finding the volume of cone,

Substituting the values in formula.

$\implies \: \sf \: v = \dfrac{1}{3} \times \pi \: \times (15) {}^{2} \times 20$

$\implies \sf \: v = \dfrac{1}{3} \times \dfrac{22}{7} \: \times (15) {}^{2} \times 20$

$\implies \sf \: v = \ \dfrac{22}{7} \: \times 75 \times 20$

$\implies \sf \: v = \dfrac{33000}{7}$

$\bf \: \underline{v =4714.28cm {}^{3} }$

So, volume of the cone is 4714.28 cm³