Question

Question :-

The ratio of height of a right circular solid cylinder and length of radius of base is 3:1. If the volume of the cylinder is 1029π cubic cm, what will be the total surface ares of the cylinder?​

Answer 1

Answer:

Given :-

• The ratio of height of a right circular solid cylinder and length of radius of base is 3:1.
• Volume of the cylinder is 1029π sq.cm.

To Find :-

• What is the total surface area of the cylinder.

Formula Used :-

➲ Volume of cylinder = πr²h

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

where,

• r = Radius
• h = Height

Solution :-

Let, the height of a right circular cylinder be 3x

And, the length of radius of base will be x cm

Now, according to the question by using the formula we get,

↦ πr²h = 1029π

↦ π × x × x × 3x = 1029π

↦ 3x³ = 1029

↦ x³ = 1029/3

↦ x³ = 343

↦ x = (7)³

➠ x = 7 cm

Hence, the required radius and height are :

✪ Radius of base :

↦ x cm

➠ 7 cm

And,

✪ Height of a right circular cylinder :

↦ 3x

↦ 3(7) cm

↦ 3 × 7 cm

➠ 21 cm

Now, we have to find the total surface area of cylinder :

Given :

• Height = 21 cm
• Radius = 7 cm

According to the question by using the formula we get,

⇒ T.S.A of cylinder = 2 × 22/7 × 7(21 + 7) sq.cm

⇒ T.S.A of cylinder = 2 × 22/7 × 7(28) sq.cm

⇒ T.S.A of cylinder = 44 × 28 sq.cm

➦ T.S.A of cylinder = 1232 sq.cm

∴ The total surface area or TSA of cylinder is 1232 sq.cm.