Question

A cylinder has height 35 cm and radius 14 cm. Find the ratio of the total surface area and curved surface area. Give me answer


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Answer 1

Answer:

7:5

Step-by-step explanation:

Height of the cylinder = 35cm

Raduis of cylinder = 14cm

Therefore,

Total surface area of cylinder = 2pier(h+r)

Curved surface area = 2pierh

Ratio = 2pier(h+r)/ 2pierh

= (h+r) / h

= (35+14)/35

= 49/35

= 7/5

That is = 7:5

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

Radius of cylinder, r = 14 cm

Height of cylinder, h = 35 cm

Now, Curved Surface Area of cylinder is given by

$\rm \: CSA_{(Cylinder)}$

$\rm \: = \: 2\pi \: rh$

$\rm \: = \: 2 \times \dfrac{22}{7} \times 14 \times 35$

$\rm \: = \: 2 \times 22 \times 2 \times 35$

$\rm \: = \: 44 \times 70$

$\rm \: = \: 3080 \: {cm}^{2}$

$\color{green}\rm\implies \:\boxed{ \rm{ \:CSA_{(Cylinder)} \: = \: 3080 \: {cm}^{2} \: }}$

Now, Total Surface Area of cylinder is given by

$\rm \: TSA_{(Cylinder)}$

$\rm \: = \: 2\pi \: r(h + r)$

$\rm \: = \: 2 \times \dfrac{22}{7} \times 14 \times (14 + 35)$

$\rm \: = \: 2 \times 22 \times 2 \times 49$

$\rm \: = \: 4312 \: {cm}^{2}$

$\color{green}\rm\implies \:\boxed{ \rm{ \:TSA_{(Cylinder)} \: = \: 4312 \: {cm}^{2} \: }}$

Now, Consider

$\rm \: TSA_{(Cylinder)} : CSA_{(Cylinder)}$

$\rm \: = \: 4312 : 3080$

$\rm \: = \: 7 : 5$

Hence,

$\color{green}\rm\implies \: TSA_{(Cylinder)} : CSA_{(Cylinder)} = 7 : 5$

$\rule{190pt}{2pt}$

Alternative Method :-

$\rm \: TSA_{(Cylinder)} : CSA_{(Cylinder)}$

$\rm \: = 2\pi \: r(r + h) : 2\pi \: rh$

$\rm \: = \: r + h : h$

$\rm \: = \: 14 + 35 : 35$

$\rm \: = \: 49 : 35$

$\rm \: = \: 7 : 5$

Hence,

$\color{green}\rm\implies \: TSA_{(Cylinder)} : CSA_{(Cylinder)} = 7 : 5$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$