Volume of Hemisphere

Q.

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

Q.

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Q.

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

1. 0.363 litres

2. 0.903 litres

3. 0.303 litres

4. 0.307 litres

Q.

A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is

1. $\sqrt{2}:1$

2. $1:2$

3. $2:1$

4. $4:1$

Q.

A cubical block of side $7$ cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Q.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere ?

Q.

A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. Find the volume of steel used in making the bowl.

Q.

A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length, is made to turn round on the longer side.Find the volume of the solid, thus generated.Also, find its curved surface area.

Q. Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16cm\times 8cm\times 8cm$. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[use\pi -31.4]$

1. $216c{m}^3$
2. $488c{m}^3$
3. $400c{m}^3$
4. $288c{m}^3$

Q.

The volume of a sphere is $1.76{\mathrm{cm}}^3$. The volume of $25$ such spheres taking into account the significant figures is

1. $0.44\times {10}^2\mathrm{cu}.\mathrm{cm}$

2. $44.00\mathrm{cu}.\mathrm{cm}$

3. $44.0\mathrm{cu}.\mathrm{cm}$

4. $44\mathrm{cu}.\mathrm{cm}$

Q.

A hemisphere made of lead of radius $7cm$ is cast into a right circular cone of height $49cm.$ Find the radius of the base of the cone.

Q.

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Q.

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If thickness of iron is $1cm$, find the volume of air filled inside the ball.

1. 3051.08 cm³
2. 3053.08 cm³
3. 3054.08 cm³
4. 3052.08 cm³

Q. A storage tank consists of a circular cylinder with a hemisphere at join on either end .if the external diameter of the cylinder be 1.4 M and its length be 8 m. find the cost of painting it on the outside at the rate rupees 10 per metre square.

Q.

A heap of wheat is in the form of a cone whose diameter is $10.5m$ and height is $3m$. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas.

Q.

Question 7
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1:2:3.

Q.

Question 7
The diameter of the moon is approximately one-fourth of the diameter of the earth.

Find the ratio of their surface area.

Q.

An ice cream vendor puts a hemispherical scoop of ice cream on a cone which has radius 7 cm and height 15 cm. Find the volume of ice cream put on the cone.

1. $702.05c{m}^3$

2. $700c{m}^3$

3. $733.33c{m}^3$

4. $718.66c{m}^3$

Q.

A conical pit of top diameter$3.5m$ is $12m$ deep. What is its capacity in kiloliters? (Assume$\mathrm{\pi }=22/7$).

Q. If a hemisphere of radius 21 cm is melted and recast to form a cone of height 42 cm, then the radius of cone is ___.

1. 10 cm
2. 16 cm
3. 14 cm
4. 21 cm

Q.

A hemisphere lead of radius 9 cm is cast into a right circular cone of height 72 cm. The radius of the base of cone is

1. 6 cm

2. 4.5 cm

3. 5.4 cm

4. 3 cm

Q.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height.
Show that their volumes are in the ratio $1:2:3$.

Q.

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Q.

Curved surface area of a hemisphere is $905\frac{1}{7}c{m}^3$, what is its volume?

Q.

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Q. A toy is in the shape of cone mounted on hemisphere of same base radius. If the volume of the toy is $231{cm}^3$ and its diameter is $7cm$, find the height of the toy.

Q.

Question 4
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilo litres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

Q. If the total surface area of a solid hemisphere is $462{cm}^2$, find its volume. (Take $\pi =22/7$)

Q.

A hemispherical bowl is made of steel, $0.25cm$ thick. The inner radius of the bowl is $5cm$. Find the outer curved surface of the bowl. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Q. The door of a building is in the form of a hemisphere its radius is 63 deci metre. find the cost of painting it at the rate of rupees 2 per square metre.