Maths-

General

Easy

Question

# A hemisphere , cylinder and a cone have equal base diameters and have the same height. Prove that their volumes are in the ratio 2:3:1

Hint:

### Volume of cylinder

## The correct answer is: 1:2:3

### Explanation:

- We have given a hemisphere, a cylinder and a cone have equal base diameters and the same height.
- We have to prove that their volumes are in ration 2:3:1

Step 1 of 1:

Volume of cone will be

Volume of hemisphere will be

Volume pf a cylinder is

It is given that the hemisphere, a cylinder and a cone have equal base diameters and the same height.

It means r = h

So,

The ratio will be

1:2:3

### Related Questions to study

Maths-

### A solid is in the form of a right circular cylinder with hemisphere at one end and a cone at the other end. Their common diameter is 3.5 cm and the height of the cylindrical and conical portions are 10 cm and 6 cm respectively .Find the volume of the solid ?

### A solid is in the form of a right circular cylinder with hemisphere at one end and a cone at the other end. Their common diameter is 3.5 cm and the height of the cylindrical and conical portions are 10 cm and 6 cm respectively .Find the volume of the solid ?

Maths-General

Maths-

### Find the circumference of a circle with radius 16 m

### Find the circumference of a circle with radius 16 m

Maths-General

Maths-

### The graph of inequality x ≤ 6 plotted on a number line represents a ____.

### The graph of inequality x ≤ 6 plotted on a number line represents a ____.

Maths-General

Maths-

### A metal container on the form of a cylinder surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m, Calculate the internal volume of the container in cubic meter ?

### A metal container on the form of a cylinder surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m, Calculate the internal volume of the container in cubic meter ?

Maths-General

Maths-

### Find the height of a triangle if its area is 125 sq.cm. and base is 10 cm.

### Find the height of a triangle if its area is 125 sq.cm. and base is 10 cm.

Maths-General

Maths-

### Which of the following points lie on the line 2x – 5y = 12?

### Which of the following points lie on the line 2x – 5y = 12?

Maths-General

Maths-

### Find the area of square inscribed in a circle of radius 8 cm.

### Find the area of square inscribed in a circle of radius 8 cm.

Maths-General

Maths-

### A hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.

### A hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.

Maths-General

Maths-

### Bloom’s category: Application

Level: Medium

Does the point P (2, -3) lie on the line -3x + y + 9= 0?

### Bloom’s category: Application

Level: Medium

Does the point P (2, -3) lie on the line -3x + y + 9= 0?

Maths-General

Maths-

### Find the area of triangle ABC

### Find the area of triangle ABC

Maths-General

Maths-

### An iron sphere of diameter 12 cm is dropped into a cylindrical can of diameter 24 cm containing water. Find the rise in the level of water when the sphere is completely immersed?

### An iron sphere of diameter 12 cm is dropped into a cylindrical can of diameter 24 cm containing water. Find the rise in the level of water when the sphere is completely immersed?

Maths-General

Maths-

### A Sphere and cube have the same surface. Show that the ratio of the volume of the sphere to that of the cube is

### A Sphere and cube have the same surface. Show that the ratio of the volume of the sphere to that of the cube is

Maths-General

Maths-

### Find the width of a 10 m long rectangular court if its boundary is 34 m.

### Find the width of a 10 m long rectangular court if its boundary is 34 m.

Maths-General

Maths-

### Bloom’s category: Application

Level: Medium

Name three points that are coplanar but not collinear.

### Bloom’s category: Application

Level: Medium

Name three points that are coplanar but not collinear.

Maths-General

Maths-

### Find the length of a rectangle whose area is 258 m2 and width is 6 m.

### Find the length of a rectangle whose area is 258 m2 and width is 6 m.

Maths-General