Volume of a Hemisphere

Q.

A conical vessel, with a base radius of $5cm$ and a height $24cm$, is full of water. This water is emptied into a cylindrical vessel of base radius $10cm$. Find the height to which the water will rise in the cylindrical vessel.

Q.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Then, the ratio of their volumes is 1:2:8.

1. True

2. False

Q.

16 hemispheres of radius 2 cm are melted to make a single sphere. Find the radius of the sphere.

1. 8 cm
2. 16 cm
3. 4 cm
4. 32 cm

Q. A hemispherical vessel of radius 7 m is filled with water. Find the amount of water (in litres) in the vessel.
(1000 litres = 1 m${}^3$)

1. 718670

Q.

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the inside surface area of the dome,
$[Assume\pi =\frac{22}{7}]$

1. $149.48m^2$

2. $209.48m^2$

3. $289.48m^2$

4. $249.48m^2$

Q. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?

1. $2:3:1$
2. $3:4:5$
3. $3:5:7$
4. $1:2:3$

Q.

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
$[Assume\pi =\frac{22}{7}]$

1. Volume = $=0.06348m^3$

2. Volume = $=1.06348m^3$

3. Volume = $=10.06348m^3$

4. Volume = $=0.09348m^3$

Q. A hemispherical vessel of radius 7 m is filled with water. The amount of water in vessel is _____.(approx)
(1000 litres = 1 m${}^3$)

1. 718670 litres
2. 71800 litres
3. 710800 litres
4. 701800 litres

Q. A hemispherical vessel of radius 7 m is filled with water. Find the amount of water (in litres) in the vessel.
(1000 litres = 1 m${}^3$)

1. 718670

Q.

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
$[Assume\pi =\frac{22}{7}]$

1. 0.903 litres

2. 0.307 litres

3. 0.363 litres

4. 0.303 litres

Q.

The volume of two hemispheres are in the ratio of 8:27. Find the ratio of their radii.

1. 3:2
2. 1:3
3. 4:3
4. 2:3

Q. Volume of a hemisphere of radius 'r' is half of volume of a sphere with same radius.

1. True
2. False

Q. A spherical shell 2 m thick has an outer diameter of 12 m. Find the volume of the material of which it is made.

1. $232.66\pi m^3$
2. $212.66\pi m^3$
3. $202.66\pi m^3$
4. $242.66\pi m^3$

Q.

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

Q.

A jar containing $2695c{m}^3$ of juice is used to fill smaller hemispherical bowls having radius 3.5 cm. Find the number of bowls that can be filled.

1. 8

2. 10

3. 30

4. 15