Question

The surface area of cylinder is 1980 CM² and the radius of its base is 15cm. Find the height of the cylinder (.(π= 3.14))

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Answer 1

${ \large{ \underline{ \pmb{ \frak{Given : }}}}}$

★ The surface area of cylinder is 1980 CM²

★ the radius of the of the cylinder base is 15cm.

★ Take the value of the symbol π as 3.14

${ \large{ \underline{ \pmb{ \frak{ To \: Find : }}}}}$

★ The hieght of the given cylinder with the surface area and radius of the base 1980cm² and 15cm respectively

${ \large{ \underline{ \pmb{ \frak{Let's \: understand \: the \: concept : }}}}}$

☀️Concept : We have said that the surface area of the cylinder is 1980cm² and the base of it 15cm, so, here we have to apply suitable formulae

❍ which include the measurements of the radius, hieght and the surface area and will help us in finding the hieght of the cylinder.

${ \large{ \underline{ \pmb{ \frak{ Using \: the \: concept : }}}}}$

★ The formula to find the surface area of a cylinder is 2πrh + 2πr² according to the given measurements and here r and h denote the radius and the hieght of the cylinder respectively

${ \large{ \underline{ \pmb{ \frak{ Solution : }}}}}$

 ★ The hieght of the cylinder is 1.31cm

${ \large{ \underline{ \pmb{ \frak{Full \: Solution : }}}}}$

 ✦ Now let's use the above mentioned formula to find the hieght of the cylinder using transposition method

❂ Total surface area of a cylinder = 2πrh + 2πr²

➼ T.S.A = 2πrh + 2πr²

➼ 1980cm² = 2 × 3.14 × 15 × h + 2 × 3.14 × 15²

➼ 1980cm² = 94.2cm × h + 1413cm

➼ 1980cm² = 1507.2cm × h

➼ h = 1.31cm

• Henceforth, the hieght of the cylinder is 1.31cm

${ \large{ \underline{ \pmb{ \frak{Diagram : }}}}}$

❍ Cylinder :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{15m}}\put(9,17.5){\sf{1.31cm}}\end{picture}$

Answer 2

❂ Total surface area of a cylinder = 2πrh + 2πr²

➼ T.S.A = 2πrh + 2πr²

➼ 1980cm² = 2 × 3.14 × 15 × h + 2 × 3.14 × 15²

➼ 1980cm² = 94.2cm × h + 1413cm

➼ 1980cm² = 1507.2cm × h

➼ h = 1.31cm

Henceforth, the hieght of the cylinder is 1.31cm