The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm² and 462 cm³ respectively. Find its diameter and its length.

Given:

Curved surface area of cylindrical toy = 132 cm²

Volume of cylindrical toy = 462 cm³

As we know that curved surface area cylinder = 2πrh

⇒ 2πrh = 132

⇒ πrh = $\dfrac{132}{2}$

⇒ πrh = 66 ……………(1)

And, volume of cylinder = πr²h

⇒ πr²h = 462

⇒ πrh x r = 462

Putting the value of 'πrh' from equation (1), we get

⇒ 66 x r = 462

⇒ r = $\dfrac{462}{66}$

⇒ r = 7 cm

Diameter = 2 x r

= 2 x 7 cm = 14 cm

Putting the value of r in equation (1),

$⇒ \dfrac{22}{7} \times 7 \times h = 66\\[1em] ⇒ \dfrac{22}{\cancel{7}} \times \cancel{7} \times h = 66\\[1em] ⇒ 22 \times h = 66\\[1em] ⇒ h = \dfrac{66}{22}\\[1em] ⇒ h = 3$

Hence, the diameter of cylinder is 14 cm and the length is 3 cm.