The surface area of a sphere is 2464 cm
2
. Calculate its volume. (Use π=
7
22
)
- A11598.67 cm
3 - B11498.67 cm
3 - C11488.67 cm
3 - D11478.67 cm
3
Solution & Step-by-step Explanation
The formula for the surface area of a sphere is:
Surface Area=4πr
2
Given that the surface area is 2464 cm
2
:
4×
7
22
×r
2
=2464
7
88
×r
2
=2464
r
2
=
88
2464×7
r
2
=28×7
r
2
=196
r=14 cm
Now, the volume of a sphere is given by the formula:
Volume=
3
4
πr
3
Volume=
3
4
×
7
22
×14×14×14
Volume=
3
4
×22×2×14×14
Volume=
3
4
×44×196
Volume=
3
34496
≈11498.67 cm
3
Surface Area=4πr
2
Given that the surface area is 2464 cm
2
:
4×
7
22
×r
2
=2464
7
88
×r
2
=2464
r
2
=
88
2464×7
r
2
=28×7
r
2
=196
r=14 cm
Now, the volume of a sphere is given by the formula:
Volume=
3
4
πr
3
Volume=
3
4
×
7
22
×14×14×14
Volume=
3
4
×22×2×14×14
Volume=
3
4
×44×196
Volume=
3
34496
≈11498.67 cm
3