Question

If a cone of height 8 M has a curved surface area of 188.4 m² then find the radius of its base and find its volume. (π-3.14)


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Answer 1

Given :-

If a cone of height 8 M has a curved surface area of 188.4 m²

To Find :-

Radius

Volume

Solution :-

We know that

l² = r² + h²

l² = r² + (8)²

l² = r² + 64

l = √(r² + 64)

Now,

188.4 = 3.14 × r × √(r² + 64)

188.4/3.14 = r × √(r² + 64)

60 = r × √(r² + 64)

Squaring both side

(60)² = [r × √(r² + 64)]²

3600 = r²(r² + 64)

3600 = r⁴ + 64r²

0 = r⁴ + 64r² - 3600

0 = r⁴ + (100r² - 36r²) - 3600

0 = r⁴ + 100r - 36r² - 3600

0 = (r² + 100)(r² - 36)

Either

r² = -100

or

r² = 36

As length can't be negative

r² = 36

r = √36

r = 6

Now

Volume of cone = 1/3 × π × r² × h

Volume = 1/3 × 22/7 × (6)² × 8

Volume = 22/21 × 36 × 8

Volume = 22/7  × 12 × 8

Volume = 2112/7

Volume = 301.7 m³