Question

The total surface area of a solid cylinder is 231 cm³ and its curved surface area is 2/3of the total surface area. Find the volume of the cylinder.​

Answer 1

Answer:

$\tt\huge{Solution:}$

Given that :-

• Total area of a solid cylinder is 231 cm^3
• Curved surface area is 2/3 of total.

To find :-

• Volume of the cylinder.

$\huge\color{blue}{Answer:-}$

•TSA =231 (given)

•CSA = 2/3 of TSA

= 2/3×231 = 154

•2πrh = 154

•TSA = 2πrh + 2πr^2

231= 154+2×22/7×r^2

231-154= 44/7r^2

77×7/44 = r^2

√49/4 = r

7/2 = r

3.5 = r

•CSA =154

2πrh = 154

2×22/7×35/10×h = 154

h = 7 cm

•now Volume = πr^2h

= 22/7 × 35/10×35/10×7

= 49×11/2

= 539/2

$\huge{= 269.5 cm^3}$

Answer 2

Answer:

Volume of cylinder = 269.5 cm³

Step-by-step explanation:

$\bold{\underline{\underline{Solution \::}}}$

Given :

Total surface area of cylinder = 231 cm³ and it's curved surface area is 2/3 of the total surface area.

Find :

Volume of the cylinder.

According to question,

Curved surface area of cylinder = 2/3 of Total surface area of cylinder.

⇒ $\dfrac{2}{3}\:\times\:231$

⇒ $77\:\times\:2$

⇒ $154$ cm²

(Curved surface area of cylinder = 2πrh)

Total surface area of cylinder = 2πrh + 2πr²

⇒ $231\:=\:154\:+\:2\:\dfrac{22}{7}\:\times\:r^2$

⇒ $231\:-\:154\:=\:\dfrac{44}{7}\:r^2$

⇒ $77\:=\:\dfrac{44}{7}\:r^2$

⇒ $r^2\:=\:\dfrac{539}{44}$

⇒ $r^2\:=\:\dfrac{49}{4}$

⇒ $r\:=\:\dfrac{7}{2}$

⇒ $r\:=\:3.5$ cm

Again,

Curved surface area of cylinder = 2πrh

⇒ $154\:=\:2\:\times\:\dfrac{22}{7}\:\times\:3.5\:\times\:h$

⇒ $154\:=\:22\:\times\:h$

⇒ $h\:=\:7$ cm

Volume of cylinder = π²rh

⇒ $\dfrac{22}{7}\:\times\:(3.5)^2\:\times\:7$

⇒ $\dfrac{1886.5}{7}$

⇒ $\bold{269.5}$ cm³