The volume of a hemisphere is 24251
2
cm3
. Find its
curved surface area.
Answers
Answer:
The curved surface area of hemisphere is 693 cm².
Step-by-step explanation:
The volume of hemisphere is 2425\frac{1}{2}2425
2
1
.
2425\frac{1}{2}=2425.52425
2
1
=2425.5
Volume of hemisphere:
V=\dfrac{2}{3}\pi r^3V=
3
2
πr
3
Substitute V=2425.5 and \pi=\frac{22}{7}π=
7
22
in above formula.
2425.5=\dfrac{2}{3}(\frac{22}{7})r^32425.5=
3
2
(
7
22
)r
3
2425.5=\dfrac{44}{21}r^32425.5=
21
44
r
3
Multiply both sides by 21.
2425.5\times 21=44r^32425.5×21=44r
3
50935.5=44r^350935.5=44r
3
Divide both sides by 44.
\dfrac{50935.5}{44}=r^3
44
50935.5
=r
3
1157.625=r^31157.625=r
3
Taking cube root on both sides.
10.5=r10.5=r
The radius of the hemisphere is 10.5.
Curved surface area of a hemisphere is
A=2\pi r^2A=2πr
2
Substitute r=10.5 and \pi=\frac{22}{7}π=
7
22
in the above formula.
A=2(\frac{22}{7})(10.5)^2A=2(
7
22
)(10.5)
2
A=693A=693