Question

Volume of cylinder is 84πrcm^2 and height is 7 cm find the TSA of cylinder​

Answer 1

Answer:

• T.S.A of cylinder = 456π cm²

Explanation:

Given information,

Volume of cylinder is 84πr cm² and height is 7 cm. Find the TSA of cylinder.

• Volume of cylinder = 84πr cm²
• Height of cylinder = 7 cm
• T.S.A of cylinder = ?

Using formula,

✪ Volume of cylinder = πr²h ✪

Where,

• r denotes radius of cylinder
• h denotes height of cylinder

We have,

• Height of cylinder (h) = 7 cm
• Volume of cylinder = 84πr cm²
• Radius of cylinder (r) = ?

Putting all values,

➻ 84πr = πr²(7)

➻ 84 × π × r = π × r × r × 7

➻ 84 = r × 7

➻ 84/7 = r

➻ 12 = r

➻ r = 12

• Hence, radius of cylinder is 12 cm.

Using formula,

✪ T.S.A of cylinder = 2πr(r + h) ✪

Where,

• r denotes radius of cylinder
• h denotes height of cylinder

We have,

• Height of cylinder (h) = 7 cm
• Radius of cylinder (r) = 12 cm
• T.S.A of cylinder = ?

Putting all values,

➻ T.S.A of cylinder = 2 × π × 12(12 + 7)

➻ T.S.A of cylinder = 2 × 12 × π(19)

➻ T.S.A of cylinder = 24 × π × 19

➻ T.S.A of cylinder = 24 × 19 × π

➻ T.S.A of cylinder = 456 × π

➻ T.S.A of cylinder = 456π cm²

• Henceforth, T.S.A of cylinder is 456π cm².

▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Answer:

✩ Given :

• Volume of cylinder = 84πr cm²
• Height of cylinder = 7 cm

✩ To Find :

• T.S.A of cylinder = ?

✩ Solution :

★ We have,

• Height of cylinder (h) = 7 cm
• Volume of cylinder = 84πr cm²
• Radius of cylinder (r) = ?

★ Finding radius

⇒ 84πr = πr²(7)

⇒ 84 × π × r = π × r × r × 7

⇒ 84 = r × 7

⇒ 84/7 = r

⇒ 12 = r

⇒ radius = 12

Hence, radius of cylinder is 12 cm.

★ Finding T.S.A of cylinder

⇒ TSA of cylinder = 2 × π × 12(12 + 7)

⇒ TSA of cylinder = 2 × 12 × π(19)

⇒ TSA of cylinder = 24 × π × 19

⇒ TSA of cylinder = 24 × 19 × π

⇒ TSA of cylinder = 456 × π

⇒ TSA of cylinder = 456π cm²

Henceforth, T.S.A of cylinder is 456π cm².

✩ Formula Used :

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πr(r + h)

✩ Extra Information :

• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²