Question

Find the volume, curved surface area and the total surface area of a cone whose height is 6cm and slant height 100cm. (Take π = 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 = √(l² – h²)

By substituting the values

Radius of the cone = √(10² – 6²)

On further calculation

Radius of the cone = √(100 – 36) = √ 64

So we get

Radius of the cone = 8cm

We know that

Volume of the cone = 1/3 πr²h

By substituting the values

Volume of the cone = 1/3 × 3.14 × 8² × 6

On further calculation

Volume of the cone = 401.92 cm³

We know that

Curved surface area of a cone = πrl

By substituting the values

Curved surface area of a cone = 3.14 × 8 × 10

So we get

Curved surface area of a cone = 251.2 cm²

We know that

Total surface area of cone = πr (l + r)

By substituting the values

Total surface area of cone = 3.14 × 8 × (10 + 8)

On further calculation

Total surface area of cone = 3.14 × 8 × 18

So we get

Total surface area of cone = 452.16 cm²