Question

the curved surface area of a cylindrical pipe is 550²cm. if the height of the pipe 25 cm .find the diameter of base.​

Answer 1

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Given:

• C.S.A. of cylinder = 550cm²
• Height of the pipe = 25 cm

To Find:

• Diameter of base

Diagram:

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

Solution:

$C.S.A.\: of \:cylinder = 2*\pi*(d/2)*h \:\:\:\:\:\:\:\:\:\:(d\:is\:diameter) \\ \\ \implies 550cm^2 = \pi*d*h \\ \\ \implies 550cm^2 = \dfrac{22}{7}*d*25 \\ \\ \implies d = \dfrac{550\!\!\!\!\!\bold{/}^{\:\:\:25\!\!\!\!\bold{/}^\:\:{1}}*7}{22\!\!\!\!\bold{/}_{1}*25\!\!\!\!\bold{/}_{1}} \\ \\ \bold{ \implies d = 7cm }$

Formula used:

• CSA of cylinder = 2πrh

Learn More:

• Volume of cylinder = πr²h

• T.S.A of cylinder = 2πrh + 2πr²

• Volume of cone = ⅓ πr²h

• C.S.A of cone = πrl

• T.S.A of cone = πrl + πr²

• Volume of cuboid = l × b × h

• C.S.A of cuboid = 2(l + b)h

• T.S.A of cuboid = 2(lb + bh + lh)

• C.S.A of cube = 4a²

• T.S.A of cube = 6a²

• Volume of cube = a³

• Volume of sphere = (4/3)πr³

• Surface area of sphere = 4πr²

• Volume of hemisphere = ⅔ πr³

• C.S.A of hemisphere = 2πr²

• T.S.A of hemisphere = 3πr²

Hope it helps!!