Question

The ratio between the radius of the base and the height of a
cylinder is 2 : 3. Find the total surface area of the cylinder, if its
volume is 1617

Answer 1

Answer:

Given :-

• The ratio between the radius of the base and the height of a cylinder is 2 : 3.
• Volume of the cylinder is 1617 cm².

To Find :-

• What is the total surface area of the cylinder.

Formula Used :-

$\clubsuit$ Volume Of Cylinder :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: Of\: Cylinder =\: {\pi}r^2h}}}$

$\clubsuit$ Total surface area of Cylinder :

$\longmapsto \sf\boxed{\bold{\pink{T.S.A\: of\: Cylinder =\: 2{\pi}r(h + r)}}}$

where,

• r = Radius
• h = Height

Solution :-

Let,

$\mapsto$ Base of the radius = 2x cm

$\mapsto$ Height = 3x cm

According to the question by using the formula we get,

$\implies \sf \dfrac{22}{7} \times (2x)^2 \times 3x =\: 1617$

$\implies \sf \dfrac{22}{7} \times 4x^2 \times 3x =\: 1617$

$\implies \sf \dfrac{22}{7} \times 12x^3 =\: 1617$

$\implies \sf x^3 =\: \dfrac{1617 \times 7}{22 \times 12}$

$\implies \sf x^3 =\: \dfrac{\cancel{11319}}{\cancel{264}}$

$\implies \sf x^3 =\: 42.875$

$\implies \sf x =\: \sqrt[3]{42.875}$

$\implies \sf \bold{\green{x =\: 3.5\: cm}}$

Hence, the required base of the radius and height are :

$\dashrightarrow$ Base of the radius :

$\leadsto \sf 2(3.5)\: cm$

$\leadsto \sf\bold{\purple{7\: cm}}$

$\dashrightarrow$ Height :

$\leadsto\sf 3(3.5)\: cm$

$\leadsto \sf\bold{\purple{10.5\: cm}}$

Now, we have to find the total surface area of the cylinder :

Given :

• Radius = 7 cm
• Height = 10.5 cm

According to the question by using the formula we get,

$\implies \sf T.S.A\: of\: Cylinder =\: 2 \times \dfrac{22}{7} \times 7(10.5 + 7)$

$\implies \sf T.S.A\: of\: Cylinder =\: \dfrac{44}{7} \times 7(17.5)$

$\implies \sf T.S.A\: of\: Cylinder =\: \dfrac{44}{7} \times 122.5$

$\implies \sf T.S.A\: of\: Cylinder =\: \dfrac{\cancel{5390}}{\cancel{7}}$

$\implies \sf\bold{\red{T.S.A\: of\: Cylinder =\: 770\: cm^2}}$

$\therefore$ The total surface area or TSA of cylinder is 770 cm².

$\rule{150}{2}$

#Learn more :

A Metallic cuboid is of Dimensions 11cm x12cm x 2.5cm was melted and cast into a Cylinder of height 100cm, what is its radius?

https://brainly.in/question/39902616

Answer 2

$\huge{\textbf{\textsf{{✩Gi}}{\purple{ve}}{\pink{n }\: {{}{:}}}}}$

★The ratio between the radius of the base and the height of a cylinder is 2 : 3.

★Volume of the cylinder = 1617.

$\huge{\textbf{\textsf{{✩To}} \: {\purple{Fi}}{\pink{nd }\: {{}{:}}}}}$

★The total surface area of the cylinder.

$\huge{\textbf{\textsf{{✩So}}{\purple{lut}}{\pink{ion }\: {{}{:}}}}}$

★Let the base and the height of the cylinder be 2x and 3x.

★We know that the volume of cylinder is πr²h.

Applying condition:-

$\implies \frac{22}{7} \times (2x) {}^{2} \times 3x = 1617$

$\implies \frac{22}{7} \times (2x \times 2x) \times 3x = 1617$

$\implies \frac{22}{7} \times 4x {}^{2} \times 3x = 1617$

$\implies 4x {}^{2} \times 3x = 1617 \times \frac{7}{22}$

$\implies \: 12x {}^{3} = 1617 \times \frac{7}{22}$

$\implies \: {x}^{3} = 1617 \times \frac{7}{22} \times \frac{1}{12}$

$\implies \: {x}^{3} = \frac{11319}{264}$

$\implies \: {x}^{3} = 42.875$

$\implies \: x = {}^{3} \sqrt{42.875}$

$\implies \: x = 3.5 \: cm$

★In the starting we assumed the base = 2x

★So, the base will be 2x = 2 × x

= 2 × 3.5 cm

= 7.0 cm

= 7 cm

★And also the height will be 3x = 3 × x

= 3 × 3.5

= 10.5 cm

★So, now the height is 10.5 cm and the base is 7 cm.

We know that the surface area of cylinder = 2πr(h+r)

$= \frac{44}{7} \times 7(17.5)$

$= \frac{44}{7} \times 122.5$

$= \frac{5390}{7}$

$= 770 \: cm {}^{2}$

★Hence, the total surface area of the cylinder is 770 cm².