Question #14537

2 Answers
Nov 1, 2016

Let lateral surface area of the cone be S_l=pirlSl=πrl
And
Let base surface area of the cone be S_b=pir^2Sb=πr2

Where r is the radius of circular base and l is slant height.

By the problem we have

S_l+S_b=2712.96.....(1)

S_l-S_b=678.24......(2)

Adding (1) and (2)

2S_l=3391.2

=>S_1=1695.6

=>pixxrxxl=1695.6

=>rxxl=1695.6/pi=1695.6/3.14=540...(3)

Again subtracting (2) from (1)

=>2S_b=2034.72

=>S_b=1017.36

pixxr^2=1017.36

=>r^2=1017.36/pi=1017.36/3.14=324

=>r=18cm.....(4)

From (3) and (4)

l=540/18=30

So height of the cone

h=sqrt(l^2-r^2)=sqrt(30^2-18^2)=24cm

Volume of the cone

V=1/3xxS_bxxh

=>V=1/3xx1017.36xx24cm^3=8138.88cm^3

Nov 1, 2016

Let lateral surface area of the cone be S_l=pirl
And
Let base surface area of the cone be S_b=pir^2

Where r is the radius of circular base and l is slant height.

By the problem we have

S_l+S_b=2712.96.....(1)

S_l-S_b=678.24......(2)

Adding (1) and (2)

2S_l=3391.2

=>S_1=1695.6

=>pixxrxxl=1695.6

=>rxxl=1695.6/pi=1695.6/3.14=540...(3)

Again subtracting (2) from (1)

=>2S_b=2034.72

=>S_b=1017.36

pixxr^2=1017.36

=>r^2=1017.36/pi=1017.36/3.14=324

=>r=18cm.....(4)

From (3) and (4)

l=540/18=30

So height of the cone

h=sqrt(l^2-r^2)=sqrt(30^2-18^2)=24cm

Volume of the cone

V=1/3xxS_bxxh

=>V=1/3xx1017.36xx24cm^3=8138.88cm^3