A hemispherical bowl has diameter a 9 cm The liquid
is poured into cylindrical bottles of diameter 3 cm.
and height 3cm, if a full bowl of liquid is
filled in the bottle, find how many bottles are
required.
Answers
Answer:
Given: Diameter =9=9cm , hence radius (r)(r)== \dfrac{9}{2}
2
9
cm
Volume of of a hemispherical bowl =\dfrac{1}{2}[ \dfrac{4}{3}\pi=
2
1
[
3
4
πr^{3}]r
3
]
Here r =r= \dfrac{9}{2}
2
9
\Rightarrow⇒ Volume of hemispherical bowl =\dfrac{1}{2}[ \dfrac{4}{3}\pi=
2
1
[
3
4
π (\dfrac{9}{2})^{3}](
2
9
)
3
]
\Rightarrow⇒Volume of the bowl =\dfrac {243}{4}\pi=
4
243
π cm^{3}cm
3
Now to calculate volume of each cylindrical bottle we are given:
Diameter : 3cm3cm , hence rr =\dfrac{3}{2}=
2
3
and height (h)(h) =3=3 cm
Volume of the cylinder =\pi=πr^{2}hr
2
h
\Rightarrow⇒volume of cylinder =\pi=π (\dfrac{3}{2})^{2}\times 3(
2
3
)
2
×3
\Rightarrow⇒Volume of cylinder =\dfrac{27}{4}\pi=
4
27
π cm^{3}cm
3
Now a number of bottles == Volume of hemispherical bowl \div÷ volume of the cylinder
\Rightarrow⇒Number of bottles = \dfrac{243}{4} \pi \div \dfrac{27}{4}\pi=
4
243
π÷
4
27
π
\Rightarrow⇒ Number of bottles = 9=9
Hence 9 bottles are required.