Question

8. Find the volume, curved surface area and the total surface area of a
cone having base radius 35 cm and height 12 cm
​

Answer 1

Given:

The base radius of the cone is 35cm.

The height if the cone is 12cm.

To Find:

The volume of the cone = ?

The curved surface area of the cone = ?

The total surface area if the cone = ?

Solution:

To find the volume of the cone = ?

Volume of the cone = 1/3 πr²h.

Put the given values in the above formula.

⟹ 1/3 πr²h

⟹ 1/3 × 22/7 × 35² × 12

⟹ 22/7 × 35² × 4

⟹ 88×35²/7

⟹ 88×1225/7

⟹ 88×175

⟹ 15400cm³

∴ The volume of the cone is 15400 cm³.

Now,

Slant height of the cone = l = √(r² + h²)

⟹ √(r² + h²)

⟹ √1369

⟹ 37cm

∴ The slant height of the cone is 37cm.

Here,

CSA of the cone = πrl

⟹ 22/7 × 35 × 37

⟹ 22 × 5 × 37

⟹ 4070cm²

∴ The curved surface area (CSA) of the cone is 4070cm².

Therefore,

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

⟹ πr(l + r)

⟹ 22/7 × 35 × (37 + 35)

⟹ 22 × 5 × 72

⟹ 7920cm²

∴ Total surface area (TSA) of the cone is 7920cm².

Answer 2

is given that

Radius of the cone =35 cm

Height of the cone =12 cm

We know that

Volume of the cone =1/3πr²h

By substituting the values

Volume of the cone = 1/3×22/7×35²+12

Volume of the cone =15400 cm ²

Slant height l= √r²+h²

=√35²+12²

=√1369

=37

Curved surface area of a cone =πrl

Total surface area of cone =22/7×35×37+35

Total surface area of cone =22×5×72

So we get

Total surface area of cone =7920 cm2