Question

The volume of right circular cylinder is 448πcm^3 and height 7cm. Find the lareral surface area and total surface area

Answer 1

Answer:

CSA of the cylinder is 352 cm² and TSA of the cylinder is 754.29 cm².

Step-by-step explanation:

Given :-

• The volume of right circular cylinder is 448π cm³.
• Height is 7 cm.

To find :-

• Curved surface area and total surface area of cylinder.

Solution :-

Consider,

• Radius of the cylinder = r cm

Formula used :-

${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

• Height = 7 cm

According to the question ,

πr²h = 448π

→ r²h = 448

→ r² × 7 = 448

→ r² = 448/7

→ r² = 64

→ r = 8

★ Radius of the cylinder is 8 cm.

Formula used :-

${\boxed{\sf{T.S.A\:of\: cylinder=2\pi\:rh}}}$

Curved surface area,

= 2πrh

= 2 × (22/7) × 8 × 7 cm²

= 352 cm²

★ CSA of cylinder is 352 cm².

Formula used :-

${\boxed{\sf{TSA\:of\: cylinder=2\pi\:r(h+r)}}}$

Total surface area,

= 2πr(h+r)

= 2×(22/7)×8 (7+8) cm²

= 2×(22/7)×8×15 cm²

= 754.29 cm²

★ TSA of the cylinder is 754.29 cm².

Answer 2

Step-by-step explanation:

Volume of cylinder = πr²h

→ 448π = πr²h 

→ 448 = r²(7)

→ r² = 448/7

→ r² = 64

→ r = 8

Hence, the radius of the cylinder is 8 cm.

Curved surface area of cylinder = 2πrh

Substitute the values,

→ 2 × (22/7) × 8 × 7

→ 44 × 8

→ 352

Hence, the curved surface area of the cylinder is 352 cm².

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

Substitute the values,

→ 2 × 22/7 × 8 × (7 + 8)

→ 2 × 22/7 × 8 × 15

→ 754.28

Hence, the total surface area of the cylinder is 754.28 cm².