find the height of a right circular cylinder whose height is equal to to its base radius length and its volume is 72 pi cm to the power of 3
Answers
Answer:
Step-by-step explanation:
Consider radius as 2x cm and height as 3x cm
We know that
Volume of cylinder =πr
2
h
By substituting the values
Volume of cylinder =
7
22
×(2x)
2
×3x
On further calculation
Volume of cylinder =
7
22
×4x
2
×3x
So we get
Volume of cylinder =
7
22
×12x
3
It can be written as
1617=
7
22
×12x
3
On further calculation
12x
3
=
22
1617×7
So we get
x
3
=
22×12
1617×7
x
3
=42.875
By taking cube root
x=
3
42.865
x=3.5
By substituting the value of x
Radius =2x=2(3.5)=7cm
Height =3x=3(3.5)=10.5cm
We know that
Total surface area =2 πr(h+r)
By substituting the values
Total surface area =2×
7
22
×7(10.5+7)
On further calculation
Total surface area =44×17.5
So we get
Total surface area =770 cm
2
Therefore, the total surface area of the cylinder is 770 cm
2
.
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