Question

10. The ratio between the curved surface area and the total surface area of a
right circular cylinder is 1:2. Find the volume of the cylinder if its total
surface area is 616 cm?"​

Answer 1

GIVEN:

Ratio between the curved surface area and the total surface area of a right circular cylinder is = 1:2

TSA of the cylinder = 616cm

TO FIND:

Volume of the cylinder

SOLUTION:

We know that,

TSA of cylinder = 2πr [r + h] = 616cm

CSA of cylinder = 2πrh = 616/2 = 308cm

According to the question,

CSA : TSA = 1 : 2

=> 2πrh/2πr [r + h]= 1/2

=> h / r + h = 1/2

=> 2h = r + h

=> 2h - h = r

=> h = r -----(1)

=> CSA of cylinder = 2πrh, it can also be written as 2πr² from the eq - 1

=> 2πr² = 308

=> 2 × 22/7 × r² = 308

=> 22/7 × r² = 308/2

=> 22/7 × r² = 154

=> r² = 154 × 7/22

=> r² = 7 × 7

=> r = 7cm

Radius = 7cm

Height = 7cm [ eq - 1 ]

Volume of cylinder = πr²h

=> 22/7 × 7² × 7

=> 22 × 49

=> 1078cm³

Therefore, the volume of cylinder is 1078cm³.

Answer 2

❥${\underline{\underline{\large{\mathtt{ANSWER:-}}}}}$

Volume of cylinder is 1078 cm³.

❥${\underline{\underline{\large{\mathtt{EXPLANATION:-}}}}}$

•GIVEN :

• The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2.
• Total surface area is 616 cm²

•TO FIND :

• Volume of the cylinder.

• SOLUTION :

★ Formulas used :-

ᴥ${\boxed{\sf{\red{Curved\: surface\:area=2\pi\:r\:h}}}}$

ᴥ${\boxed{\sf{\green{Total\: surface\:area=2\pi\:r(h+r)}}}}$

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

According to the question,

$\sf{Curved\:surface\:area\::\: Total\: surface\: area=1:2}$

$\implies\sf{2\pi\:r\:h\::2\pi\:r(h+r)=1:2}$

$\implies\sf{\frac{2\pi\:r\:h}{2\pi\:r(h+r)}=\frac{1}{2}}$

$\implies\sf{\frac{h}{h+r}=\frac{1}{2}}$

$\implies\sf{h=r}$

Total surface area = 616 cm²

So , Curved surface area=616/2 cm²

→ Curved surface area = 308 cm²

Curved surface area = 2πrh

→Curved surface area=2πr²[h=r]

According to the question,

$\sf{2\pi\:r^2=308}$

$\implies\sf{\pi\:r^2=154}$

$\implies\sf{r=7}$

h=r= 7 cm

Volume of cylinder= πr²h

→volume of cylinder=22/7×7×7 ×7cm³

→Volume of cylinder=1078 cm³

Therefore, volume of the cylinder is 1078 cm³.

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