Question

The sum of the radius of the base and height of a solid right circular cylinder is
37 cm. If its total surface area is 1628 cm, find its volume.​

Answer 1

Answer:-

• The volume of cylinder is 4620cm³.

Step-by-step explaination:-

Given:

• Sum of radius and height of cylinder = 37

i.e. r + h = 37

• Total surface area = 1628cm²

To Find:

• Volume of right circular cylinder.

Solution:

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

⟶ 2 × 22/7(r + 37) = 1628

⟶ 44/7(r + 37) = 1628

⟶ r = 1628 × 7/ 44 × 37

⟶ r = 7

So, r + h = 37

⟶ 7 + h = 37

⟶ h = 37 - 7

⟶ h = 30cm

So,

Volume of cylinder = πr²h

⟶ 22/7 × (7)² × 30

⟶ 22/7 × 49 × 30

⟶ 4620cm³

Answer 2

Given :

✰ The sum of the radius of the base and height of a solid right circular cylinder is 37 cm.

✰ Total surface Area = 1628cm²

To Find :

✰ Volume of Cylinder

Solution :

✰ As it is given that sum of radius (r) and Height (h) is 37cm. So, Firstly we will find the Height and radius of the cylinder by Using the formula of Total surface area of cylinder that is given by 2πr(h + r). After Getting the radius and height of the cylinder we can find the volume of the cylinder. By using Formula of Volume of cylinder that is πr²h.

Total surface area = 2πr(h + r)

⟹ 1628 = 2 × 22/7 × r × 37

⟹ 1628 = 44/7 × r × 37

⟹ 1628/37 = 44/7 × r

⟹ 44 = 44/7 × r

⟹ r = 44/44 × 7

⟹ r = 7cm

Thus, Radius is 7cm

⟹ h + r = 37

⟹ h + 7 = 37

⟹ h = 37 - 7

⟹ h = 30cm

Height is 30cm

Volume of cylinder = πr²h

⟹ 22/7 × (7)² × 30

⟹ 22/7 × 49 × 30

⟹ 22 × 7 × 30

⟹ 4620cm³

∴ Volume of cylinder is 4620cm³