Question

the sum of the radius and height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 CM square find the height of the volume of the cylinder​

Answer 1

Answer:

Step-by-step explanation:

Given :-

The sum of the radius and height of a cylinder is 37 cm.

Total surface area of the cylinder = 1628 cm²

To Find :-

The height of the volume of the cylinder​

Formula to be used :-

Total surface area of the cylinder = 2 πr (r + h)

Volume of the cylinder = πr2h

Solution :-

Let r and h be the radius and height of the solid cylinder.

Total surface area of the cylinder = 1628 cm²

⇒ 2 πr (r + h) = 1628 cm²

⇒ 2πr × 37 = 1628 cm²

⇒ 2 × 22/7 × r × 37 = 1628 cm²

⇒ r = (1628 × 7)/(2 × 22 × 37)

⇒ r = 7 cm

Putting r value, we get

⇒ r + h = 37 cm

⇒ 7 + h = 37 cm

⇒ h = 30 cm

Volume of the cylinder = πr2h

Volume of the cylinder = 22/7 × 7 × 7 × 30

Volume of the cylinder = 4620 cm³

Hence, the height and the volume of the cylinder​ are 30 cm and 4620 cm³.