Question

the radius and height of a cylinder are in the ratio 5 is to 7 and its volume 550 cm cube find its radius​

Answer 1

》 The radius and height of a cylinder are in the ratio 5 : 7.

• Let radius of cylinder be 5M and height of cylinder be 7M.

Volume of cylinder = 550 cm³

We know that..

Volume of cylinder = $\pi {r}^{2}h$

=> 550 = $\pi {r}^{2}h$

Put the known values in above formula to find the radius of cylinder.

=> 550 = $\dfrac{22}{7}$ × (5M)² × 7M

=> 550 = $\dfrac{22}{7}$ × 25M² × 7M

=> 550 = 22 × 25M² × M

=> 550 = 550M³

=> M³ = 1

=> M = 1

So,

Radius of cylinder = 5M

=> 5(1) = 5 cm

Height of cylinder = 7M

=> 7(1) = 7 cm

Answer :-

5 cm is the radius of cylinder.

☆ VERIFICATION :

From above calculations we have M = 1

Put value of M in this : 550 = $\dfrac{22}{7}$ × (5M)² × 7M

=> 550 = $\dfrac{22}{7}$ × [5(1)]² × 7(1)

=> 550 = $\dfrac{22}{7}$ × 25 × 7

=> 550 = 550

Answer 2

Step-by-step explanation:

volume of a cylinder=πr²h=550cm³

radius and height in ratio=5:7

radius=5x

height=7y.

(if ratio is removed a constant must be added and the constant must be same that has been done in the above step )

substitute height and radius in the formula V=πr²h

550=22/7*25x²*7x

550=22/7*175x³

3850=3850x³

x³=1

x=1

substitute value of X in radius and height

radius=5x.

=5(1)

=5cm

height=7x

=7(1)

=7cm

therefore the radius and height of the cylinder with a volume 550cm³ is 5cm and 7cm respectively

hope the answer is clear