Question

The ratio between the radius of the base and height of a cylinder is 2:3. If its volume
is 1617 cm, find the total surface area of the cylinder​

Answer 1

Answer:

• TSA = 769.3 cm²

Steps:

Given that,

• Ratio of radius of the base to that of the height of the cylinder is 2:3

Let us assume, the radius to be '2x' and height to be '3x'.

Also it is given that, Volume of the given cylinder is 1617 cm³.

Applying the volume of cylinder formula we get:

$\boxed{ Volume = \pi r^2h}$

Substituting the given values, we get:

$\implies Volume = 3.14 \times (2x)^2 \times 3x\\\\\\\implies 1617 = 3.14 \times 4x^2 \times 3x\\\\\\\implies \dfrac{1617}{3.14} = 12x^3\\\\\\\implies 514.96 = 12x^3\\\\\\\implies x^3 = \dfrac{514.96}{12}\\\\\\\implies x^3 = 42.91 cm^3\\\\\\\implies x = \sqrt[3]{42.91}\\\\\\\implies \boxed{x = 3.50\: cm}$

Hence the radius of the cylinder is:

• 2x = 2 ( 3.50 ) = 7 cm

And the height of the cylinder is:

• 3x = 3 ( 3.5 ) = 10.5 cm

Hence the total surface area of the cylinder is calculated by the formula:

⇒ 2πr ( h + r )

Substituting the values we get:

→ 2 × 3.14 × 7 ( 7 + 10.5 )

→ 43.96 × 17.5

→ 769.3 cm²

Hence the total surface area of the given cylinder is 769.3 cm²

Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☞ Ratio between the radius of the base and height of a cylinder = 2 : 3

☞ Volume of cylinder = 1617 cm³

$\Large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☞ Total Surface Area (TSA) of cylinder = ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Concepts Used :-}}}}}}$

☞ Volume of cylinder = πr²h

☞ CSA of cylinder = 2πrh

☞ TSA of cylinder = 2πrh + πr² = 2πr(h + r)

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

Let the ratio between the radius of the base and height of a cylinder be 2a : 3a

∴ Radius = 2a

∴ Height = 3a

☞ Volume of cylinder = πr²h

⇒ 1617cm³ = $\dfrac{22}{7}$ × (2a)² × 3a

⇒ 1617cm³ = $\dfrac{22}{7}$ × 4a² × 3a

⇒ 1617cm³ = $\dfrac{22}{7}$ × 12a³

⇒ 1617cm³ × $\dfrac{7}{22}$ × $\dfrac{1}{12}$ = a³

⇒ 42.875cm³ = a³

⇒ $\sqrt[3]{42.875 \sf{cm}^3}$ = a

⇒ 3.5cm = a

⇒ a = 3.5cm

∴ a = 3.5 cm

» Radius = 2a

⇒ Radius = 2 × 3.5cm

⇒ Radius = 7cm

∴ Radius of cylinder = 7cm

» Height = 3a

⇒ Height = 3 × 3.5cm

⇒ Height = 10.5cm

∴ Height of cylinder = 10.5cm

☞ TSA of cylinder = 2πrh + πr² = 2πr(h + r)

☞ TSA of cylinder = 2πr(h + r)

⇒ TSA of cylinder = 2 × $\dfrac{22}{7}$ × 7cm (10.5cm + 7cm)

⇒ TSA of cylinder = 2 × $\dfrac{22}{7}$ × 7cm (17.5cm)

⇒ TSA of cylinder = 2 × $\dfrac{22}{7}$ × 7cm × 17.5cm

⇒ TSA of cylinder = 770cm²

∴ TSA of cylinder = 770cm²

∴ Total Surface Area (TSA) of cylinder is 770cm².

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Additional Information :-}}}}}}$

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

◆ NOTE : Additional Information can also be seen in the attached image.

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Learn more from Brainly :-}}}}}}$

The circumference of a base of a cylinder is 176cm and its hight is 60 cm find the volume of cylinder.

See answer at : https://brainly.in/question/32832991