The volume of a cone is 1232 cm cube and radius of the base is 7cm find it's total surface area
Answers
Answer:
Formula to get the volume of a circular cone is
V=\frac{1}{3}\pi r^{2}hV=
3
1
πr
2
h
Here r = radius of the circular base of the cone
h = height of the cone
We can get the value of h when we plug in the values of r and V in the formula given in the question.
1232=\frac{1}{3}\pi (\frac{14}{2})^{2}h1232=
3
1
π(
2
14
)
2
h
1232=\frac{1}{3}(\frac{22}{7})\times 49h1232=
3
1
(
7
22
)×49h
h=\frac{1232\times 21}{22\times 49}h=
22×49
1232×21
h = 24 cm
Now in the right angle triangle ABC,
l² = r² + h²[By Pythagoras theorem]
Where l² = 7² + 24²
l=\sqrt{49+576}l=
49+576
l = 25 cm
And curved surface area of the cone = \pi rlπrl
= (\frac{22}{7})(7)(25)(
7
22
)(7)(25)
= 550 square cm