Question

The ratio of the height to the radius of a vertical tube is 3: 1. If the volume of the funnel is 1029 cubic cm, find the total surface area of ​​the funnel.​

Answer 1

GIVEN:-

Volume of the funnel = 1029 cm^3

Ratio of height and radius of cylinder = 3:1

TO FIND:-

TSA of the funnel.

SOLUTION:-

Let the height be 3r & Radius be r.

Using the formula of the volume of cylinder,

→ πr^2h

→ π×r^2×3r

→ 3πr^3

So,

→ 3πr^3 = 1029π

→ r^3 = 1029π/3π

→ r^3 = 343

→ r = 7 cm

Therefore,

r = 7cm

h = 3×7 = 21cm

Hence,

TSA:

→ 2πr (h+r)

→ 2×22/7 (21 + 7)

→ 1232 cm²

Therefore, the required answer = 1232 cm²