Question

the circumfrence of the base and height of a right circular cylinder are 44cm and 10cm respectively. find its volume , curved surface area and total surface area ​

Answer 1

$C.S.A \: of \: Cylinder = 2\pi rh \\ C.S.A = \: 44 \times 10 \\C.S.A = 440 {cm}^{2} \\ \\ C = 2\pi r \\ 44 = 2 \times \frac{22}{7} \times r \\ r = \frac{44 \times 7}{44} \\ r = 7cm \\ \\ Volume \: of \: a \: Cylinder \: = \pi {r}^{2}h \\V = \frac{22}{7} \times 7 \times 7 \times 10 \\V = 70 \times 22 \\ = 1540 {cm}^{3} \\ \\ T.S.A \: of \: a \: Cylinder = 2\pi r(h + r) \\T.S.A = 2 \times \frac{22}{7} \times 7(10 + 7) \\T.S.A = 44 \times 17 \\T.S.A = 748 {cm}^{2}$

Answer 2

$\bold{\underline{\underline{\huge{ANSWER\::}}}}$

Given:

The circumference of the base and height of a right circular cylinder are 44cm and 10cm respectively.

To find:

• Volume of the cylinder.
• Curved surface area of the cylinder.
• Total surface are of the cylinder.

Explanation:

$\bold{\underline{\underline{\huge{\sf{CASE\:1:}}}}}$

We know that volume of the cylinder: πr²h [cubic units]

We have,

• Height of the right circular cylinder= 10cm

The circumference of the base of a right circular cylinder= 44cm.

∴ Circumference= 2πr

→ 44cm = 2×22/7 ×r

→ r= $\frac{\cancel{44}*7}{\cancel{44}} =7cm$

Therefore,

Volume of the cylinder=$\frac{22}{7}$ × 7× 7× 10

Volume of the cylinder= $(\frac{22}{\cancel{7}} *\cancel{7}*7*10)cm^{3}$

Volume of the cylinder= (22× 7× 10)cm³

Volume of the cylinder= 1540cm³.

$\bold{\underline{\underline{\huge{CASE\::2}}}}}}$

We know that curved surface area of the cylinder: 2πrh sq. unit

⇒ 2 × $\frac{22}{7}$× 7cm × 10cm

⇒ $(\frac{44}{\cancel{7}} *\cancel{7}*10)cm^{2}$

⇒ (44 ×10)cm²

⇒ 440cm².

$\bold{\underline{\underline{\huge{CASE\::3}}}}}$

We know that the total surface area of the cylinder: 2πr(r+h) sq. unit

Total surface area of the cylinder=$[2*\frac{22}{7} *7(7+10) ]cm^{2}$

Total surface area of the cylinder= $(\frac{44}{\cancel{7}} *\cancel{7}*17)cm^{2}$

Total surface area of the cylinder= (44× 17)cm²

Total surface area of the cylinder= 748cm².