Question

A right circular cone of height 4cm has a curved surface area 47.1 sq cm. Find its volume

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

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

Again given curve surface = 47.1

=> πrl = 47.1

=> 3.14*r*√(r2 + h2 ) = 47.1

=> r*√(r2 + h2 ) = 47.1/3.14

=> r*√(r2 + 42 ) = 15

=> r*√(r2 + 16) = 15

=> r2 *(r2 + 16) = (15)2

=> r2 *(r2 + 16) = 225

=> r4 + 16r2 = 225

=> r4 + 16r2 - 225 = 0

=> (r2 - 9)*(r2 + 25) = 0

=> r2 = 9, -25

Since r2 ≠ -25

So r2 = 9

=> r = 3

Now, volume of the cone = πr2 h/3

= {3.14*3*3*4}/3

= 3.14*3*4

= 3.14*12

= 37.68 cm3