Question

a solid cylinder has a total surface area 462 sq cm it's curved surface area is one third of the total surface area find the volume of the cylinder​

Answer 1

✬ Volume = 539 cm³ ✬

Step-by-step explanation:

Given:

• Total surface area of Cylinder is 462 cm².
• Curved surface area of cylinder is 1/3 times of total surface area.

To Find:

• What is the volume of cylinder ?

Solution: We have given TSA that is 462 cm².

★ TSA of Cylinder = 2πrh + 2πr² ★

➟ 2πrh + 2πr² = 462 cm²......(1)

★ CSA of Cylinder = 2πrh ★

➟ CSA = 1/3 of TSA

➟ 2πrh = 1/3(462) cm² = 154 cm²......(2)

Now, Put the value of 2πrh from equation (2) in equation (1).

➫ 2πrh + 2πr² = 462

➫ 154 + 2πr² = 462

➫ 2πr² = 462 – 154

➫ 2πr² = 308

➫ r² = 308/2π

➫ r² = 308/2 $\times$ 22/7

➫ r² = 308 $\times$ 7/44

➫ r² = 49

➫ r = √49 = 7 cm (Radius)

Now, put the value of radius in equation(2)

➙ 2πrh = 154

➙ 2 $\times$ 22/7 $\times$ 7 $\times$ h = 154

➙ 44h = 154

➙ h = 154/44 = 3.5 cm (Height)

As we know that

★ Volume of Cylinder = πr²h ★

$\implies{\rm }$ 22/7 $\times$ 7² $\times$ 3.5

$\implies{\rm }$ 22 $\times$ 7 $\times$ 3.5

$\implies{\rm }$ 539 cm³

Hence, Volume of Cylinder is 539 cm³.

Answer 2

Hope this will help you :)