Question

The height of a cone is 8m and its Curved Surface Area is 188.4m².Find its volume.
(Take π=3.14)​

Answer 1

Correct question:-

The height of a cone is 8m and its curved surface area is 188.4m².Find its volume (Take π = 3.14)

Given:-

→Height of the cone=8m

→C.S.A of the cone=188.4m²

→Value of π= 3.14

To find:-

→Volume of the cone

Solution:-

Let the radius be r metre and the slant height be l metres.

=>C.S.A of a cone= πrl m²

=> πr√r²+h² m²

=>(3.14×r×√r²+64)m²

=>3.14×r×√r²+64=188.4

=>r√r²+64 = 188.4/3.14

=>r√r²+64 = 60

=>r²(r²+64) = 3600

=>r²+64r²-3600 = 0

=>(r²+100)(r²-36)=0

Since,r²= -100 gives an imaginary value of r

=>r²=36

=>r=6

Hence,we got radius of base of the cone as 6m.

=>Volume of a cone= 1/3πr²h

=>1/3×3.14×6×6×8

=>904.32/3

=>301.44 m³

Thus,volume of the cone is 301.44m³.