Question

# The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

- 11
- 22
- 44
- 66

Hint:

**Hint:-** The volume of a 3 -dimensional solid is the amount of space it occupies.

The volume V of a cylinder with radius r is the area of the base B times the height h .

V = Bh or V= πr2h

## The correct answer is: 44

### Solution:-

- We have given volume of a right circular cylinder(A), V
_{1} = 22 cm^{3}
- Let R be radius of cylinder A and H be the height.
- Let the second cylinder denoted as cylinder B
- We have to find the volume of the cylinder B whose radius is twice of cylinder A

Let the radius of cylinder B be R_{2}.

So, R_{2} = 2R ---------(1)

- Height of cylinder B is half of height of cylinder A.

So, H_{2} = H/2 ---------(2)

- To find the volume of cylinder B we will have to compare the volumes of both cylinders. Let’s find equation of volume .
- We know the volume of cylinder= πr
^{2}h
- Volume of cylinder A = πR
^{2}H ----------(3)
- Volume of cylinder B = πR
_{2}^{2}H_{2}
- Substitute the values of R
_{2} and H_{2 }from equation (1) and (2) in Volume of cylinder B formula.

Volume of cylinder B = π(2R)^{2(}H/2)

= π (4R^{2})^{(}H/2)

= π (2R^{2})(H)

Volume of cylinder B = 2πR^{2}H ---------(4)

- Divide the volume of cylinder A by volume of cylinder B from equation (3) and (4).

Volume of cylinder A/ Volume of cylinder B = πR^{2}H / 2πR^{2}H

Volume of cylinder A/ Volume of cylinder B = 1/ 2

- We know the volume of cylinder A is 22 cm
^{3.}

So, 22 / Volume of cylinder B = 1/ 2

- Reciprocating both sides we get,

Volume of cylinder B / 22 = 2

- Multiplying both sides by 22 we get,

Volume of cylinder B = 44 cm^{3}

- Therefore, the volume of second cylinder is option C) 44 .

_{1}= 22 cm^{3}^{2}h^{2}H ----------(3)_{2}^{2}H_{2}_{2}and H_{2 }from equation (1) and (2) in Volume of cylinder B formula.^{3.}### Related Questions to study

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