Question

Find the volume curved surface area and the total surface area of a cone whose height is $6cm$ and slant height $100cm$ (Take $\pi =3.14$)

Answer 1

It is given that

Height of the cone $=6cm$

Slant height of the cone $b=10cm$

We know that

Radius of the cone $=\sqrt{(l^2-h^2)}$

By substituting the values

Radius of the cone $\sqrt{({10}^2-6^2)}$

On further calculation

Radius of the cone $\sqrt{(100-36)}=\sqrt{64}$

So we get

Radius of the cone $=8cm$

We know that

Volume of the cone $=\frac{1}{3}\pi r^{2}h$

By substituting the values

Volume of the cone $=\frac{1}{3}\times 3.14\times 8^2\times 6$

On further calculation

Volume of the cone $=401.92c{m}^2$

We know that

Curved surface area of a cone $=\pi rl$

By substituting the values

Curved surface area of a cone $=3.14\times 8\times 10$

So we get

Curved surface area of a cone $=251.2c{m}^2$

We know that

Total surface area of cone $=\pi r(l+r)$

By substituting the values

Total surface area of cone $=3.14\times 8\times (10+8)$

On further calculation

Total surface area of cone $=3.14\times 8\times 18$

So we get

Total surface area of cone $=424.16c{m}^2$