Question

A cone of height 8 cm has a curved surface area of 188.4 sq m if phai = 3.14 the radius of its base is

Answer 1

h= 8 from curved surface area find L then by using total surface area of cone pi rl + pi r2 you can find its radius

Answer 2

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

$\longrightarrow$ l² = r² + h²

$\longrightarrow$ l² = r² + (8)²

$\longrightarrow$ l² = r² + 64

$\longrightarrow$ l = √(r² + 64)

Now,

$\implies$188.4 = 3.14 × r × √(r² + 64)

$\implies$188.4/3.14 = r × √(r² + 64)

$\implies$60 = r × √(r² + 64)

Squaring both side

(60)² = [r × √(r² + 64)]²

3600 = r²(r² + 64)

3600 = r⁴ + 64r²

$\longrightarrow$ 0 = r⁴ + 64r² - 3600

$\longrightarrow$ 0 = r⁴ + (100r² - 36r²) - 3600

$\longrightarrow$ 0 = r⁴ + 100r - 36r² - 3600

$\longrightarrow$ 0 = (r² + 100)(r² - 36)

Either

$\implies$ r² = -100

or

$\implies$ r² = 36

As length can't be negative

$:\implies$ r² = 36

$:\implies$ r = √36

$:\implies$ r = 6

Now

$\longrightarrow$Volume of cone = 1/3 × π × r² × h

$\longrightarrow$Volume = 1/3 × 22/7 × (6)² × 8

$\longrightarrow$Volume = 22/21 × 36 × 8

$\longrightarrow$Volume = 22/7  × 12 × 8

$\longrightarrow$Volume = 2112/7

$\longrightarrow$Volume = 301.7 m³