Question

If the Total surface Area of cone is 704cm^2 and radius of its base is 7 cm find volume of the cone! Plz do fast
I will choose first correct answer as brainlist! 10 points!​

Answer 1

Given:

• The Total Surface Area of a cone is 704 cm sq.
• The radius of the base of the cone is 7 cm

To be found:

The volume of the cone.

The formula to find the volume of the cone is

$\boxed{\red{\sf{\frac{1}{3}\pi r^{2}h}\ \underline{unit\ cube.} }}$

We need, radius(given) and height,

So, we have to find the height of the cone,

By the given data we can find the slant height(l) and then we can find the height of the cone.

Now,

Total Surface Area of the cone

= πrl + πr² unit sq. OR πr (l+r) unit sq.

[In which, 'r' is the 'radius', and 'l' is the 'slant height'.]

So,

⇒ πr (l+r) = 704

$\implies \frac{22}{\not7}\times \not7 (l+7) = 704$

$\implies 22 (l+7) = 704$

$\implies (l+7) = 704 \div 22$

$\implies l+7 = 32$

$\implies l=32 - 7$

$\implies l = 25 cm$

Thus, the slant height of the cone is 25 cm

Now,

We know the relation between, slant height, height, and radius of the cone,

$\boxed{\bf{l^{2}=h^{2}+r^{2}}}$

⇒ (25)² = (h)² + (7)²

⇒ 625 = h² + 49

⇒ 625 - 49 = h²

⇒ 576 = h²

⇒ 24 = h

Therefore,

The height of the cone is 24 cm

Now,

The volume of the cone

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

$= \frac{1}{3}\times \frac{22}{\not7} \times (\not7) \times (7)\times (24)$

$= 22 \times 7 \times 8$

= 1232 cm cube

Hence,

The volume of the cone is 1232 cm cube.