The radius of the base of a solid right circular cylinder is 10.5 cm and its volume is 5197.5 cm
3
. What is the total surface area (in cm
2
) of the cylinder? (Take π=
7
22
)
- A1584
- B1683
- C1605
- D1749
Solution & Step-by-step Explanation
Given:
Radius (r) = 10.5 cm=
2
21
cm
Volume (V) = 5197.5 cm
3
=
2
10395
cm
3
The formula for the volume of a cylinder is:
V=πr
2
h
2
10395
=
7
22
×(
2
21
)×(
2
21
)×h
2
10395
=
7
22
×
4
441
×h
2
10395
=
2
11×63
×h
10395=693×h
h=
693
10395
=15 cm
Now, find the total surface area (TSA) of the cylinder:
TSA=2πr(h+r)
TSA=2×
7
22
×
2
21
×(15+10.5)
TSA=66×25.5
TSA=1683 cm
2
Radius (r) = 10.5 cm=
2
21
cm
Volume (V) = 5197.5 cm
3
=
2
10395
cm
3
The formula for the volume of a cylinder is:
V=πr
2
h
2
10395
=
7
22
×(
2
21
)×(
2
21
)×h
2
10395
=
7
22
×
4
441
×h
2
10395
=
2
11×63
×h
10395=693×h
h=
693
10395
=15 cm
Now, find the total surface area (TSA) of the cylinder:
TSA=2πr(h+r)
TSA=2×
7
22
×
2
21
×(15+10.5)
TSA=66×25.5
TSA=1683 cm
2