Question

A cone of height 8 m has a curved area 188.4 m² . find it's volume.

Answer 1

Given, height of the cone h = 8

Let r is the radius and l is the slant height of the cone.

Given curved surface area of the cone = 188.4

=> πrl = 188.4

=> πr√(r2 + h2 ) = 188.4             {since slant height l = √(r2 + h2 )}

=> 3.14*r√(r2 + 82 ) = 188.4

=> r√(r2 + 64 ) = 188.4/3.14

=> r√(r2 + 64 ) = 60

=> r2 *(r2 + 64 ) = (60)2

=> r4 + 64r2 = 3600

=> r4 + 64r2 - 3600 = 0

=> (r2 - 36)*(r2 + 100) = 0

=> r2 = 36, -100

Since square of a number can not be negative.

Hense, r2 = -100 is not possible

So, r2 = 36

=> r = ±6

Again since radius can not be negative.

So, r = 6

Now volume of the cone = (1/3)*πr2 h

                                  = (1/3)*π*62 h

                                  = (3.41*36*8)/3

                                  = 3.41*12*8

                                  = 301.44 cm3

Answer 2

Hello!

Here Is your answer !
_______________
Given

Height of the cone h = 8m√

Let r is the radius and l is the slant height of the cone

Given

Curved surface area of the cone = 188.4m2√

So according to the question!!

➡️ πrl = 188.4

➡️ πr√(r2 + h2 ) = 188.4             {since slant height l = √(r2 + h2 )}

➡️3.14 × r√(r2 + 82 ) = 188.4

➡️ r√(r2 + 64 ) = 188.4/3.14

➡️ r√(r2 + 64 ) = 60

➡️ r2 × (r2 + 64 ) = (60)2

➡️ r4 + 64r2 = 3600

➡️  r4 + 64r2 - 3600 = 0

➡️ (r2 - 36)(r2 + 100) = 0

➡️  r2 = 36, -100

Negative number is discarded!

Hence, r2 = -100 is not
possible

So, r2 = 36

So radius = 6m

Now volume of the cone = (1/3) × πr2 h

  ➡️ (1/3) × π (6)2 h

  ➡️ (3.41*36*8)/3

  ➡️ 3.41*12*8

  ➡️ 301.44m3√

Hope it helps u!