Question

The total surface area of right circular is 1760m square. the sum of its base radius and height is 40cm. find its curved surface area.​

Answer 1

Answer:

1452cm²

Step-by-step explanation:

2πr(r+h) =1760

2πr(40) = 1760 ( given sum of its base radius and

height is 40cm)

2×22\7×40r = 1760

r = 1760×7/2×22×40

r = 7 cm

if r = 7 cm

then h = 33 cm

now

curved surface area = 2πrh

= 2 ×22\7×7×33

= 44×33

= 1452 cm²

hope it helped you

Answer 2

Answer:

The curved surface area of cylinder is 1452 cm².

Step-by-step explanation:

Given :

The total surface area of right circular is 1760 m².

The sum of its base radius and height is 40cm.

To Find :

The curved surface area.

Using Formulas :

${\star{ \underline{\boxed{\sf{\pink{Tsa \: of \: cylinder = 2\pi r(r + h)}}}}}}$

• Tsa = Total surface area
• π = 22/7
• r = radius
• h = height

${\star{ \underline{\boxed{\sf{\pink{Csa \: of \: cylinder = 2\pi rh }}}}}}$

• Csa = Curved surface area
• π = 22/7
• r = radius
• h = height

Solution :

Here we have given that the tsa of right circular is 1760m² and sum of its base radius and height is 40cm. So, finding the radius and height of cylinder.

According to the question substituting all the given values in the formula :

${\implies{\sf{Tsa \: of \: cylinder = 2\pi r(r + h)}}}$

${\implies{\sf{1760= 2 \times \dfrac{22}{7} \times r(40)}}}$

${\implies{\sf{1760=\dfrac{2 \times 22}{7} \times r(40)}}}$

${\implies{\sf{1760=\dfrac{44}{7} \times r(40)}}}$

${\implies{\sf{1760=\dfrac{44}{7} \times r \times 40}}}$

${\implies{\sf{1760=\dfrac{44 \times 40}{7} \times r}}}$

${\implies{\sf{1760=\dfrac{1760}{7} \times r}}}$

${\implies{\sf{r = 1760 \times \dfrac{7}{1760}}}}$

${\implies{\sf{r = \cancel{1760} \times \dfrac{7}{\cancel{1760}}}}}$

${\implies{\sf{\red{r = 7 \: cm}}}}$

Hence, the radius of cylinder is 7 cm.

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Now, we know the radius of cylinder is 7 cm and sum of base radius and height is 40cm. So, finding the height

${\implies\sf{r + h = 40 \: cm}}$

${\implies\sf{Radius + Height = 40 \: cm}}$

${\implies\sf{7 + Height = 40 \: cm}}$

${\implies\sf{Height = 40 - 7}}$

${\implies{\sf{\red{Height = 33 \: cm}}}}$

Hence, the height of cylinder is 33 cm.

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Now, we know the radius of cylinder is 7 cm and height of cylinder is 33 cm. So, finding the curved surface area of cylinder by substituting the values in the formula :

${\implies{\sf{Csa_{(Cylinder)} = 2\pi rh }}}$

${\implies{\sf{Csa_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 7 \times 33}}}$

${\implies{\sf{Csa_{(Cylinder)} = 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7} \times 33}}}$

${\implies{\sf{Csa_{(Cylinder)} = 2 \times 22\times 33}}}$

${\implies{\sf{Csa_{(Cylinder)} = 44\times 33}}}$

${\implies{\sf{\red{Csa_{(Cylinder)} = 1452 \: {cm}^{2}}}}}$

Hence, the curved surface area of cylinder is 1453 cm².

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Learn More :

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

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