Question

A solid cylinder of height 3 cm and diameter 4 cm is melted and recast
into a solid right circular cone of diameter 6 cm. Find:
(1) height of the cone.
(ii) total surface area of the cone. Give your answer correct to one decimal
place. (Take n = 3.14)
​

Answer 1

Answer.. I hope it will be helpful for all

Answer 2

Given,

Height of the cylinder = 3 cm

Diameter of the cylinder = 4 cm

Diameter of cone = 6 cm

To find,

Height and total surface area of cone.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Radius of cylinder = 4/2 = 2 cm

Volume of cylinder = π × (2)² × 3 = 37.68 cm³

So, volume of cone = 37.68 cm³

Let, the height of cone = h cm

Radius of cone = 6/2 = 3 cm

Volume of cone = π × (3)² × h/3 = 9.42×h cm³

According to the data mentioned in the question,

9.42 × h = 37.68

h = 4

Height of cone = 4 cm

Slant height = √(4)²+(3)² = √(16+9) = √25 = 5 cm

CSA of cone = π × 3 × 5 = 47.1 cm²

TSA of cone = CSA + Base area = 47.1 + (3.14×3×3) = 47.1+28.26 = 75.36 ≈ 75.4 cm²

Hence, the height of cone is 4 cm and TSA of cone is 75.4 cm².