8. Perimeter of base of a cylinder is 5cm and its curved surface area is
10cm2
,then the height of the cylinder is -----------
A)50cm B)15cm C)2cm D)5cm
Answers
Answer:
The perimeter of base of a cylinder is 5cm
→ The curved surface area of the cylinder is 10cm²
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→ The height of the cylinder
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❍ Concept : As we have been given the perimeter ( Circumference ) of the cylinder which is 5cm and its curved surface area which is 10cm² So, now let's find the radius of the cylinder with the help of its circumference.
★ Later substitute the value of its radius in the formula to find the curved surface area and find the height of the cylinder.
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✪ Formula to find the circumference of the base :
\tt Circumference = 2 \pi rCircumference=2πr
✪ Formula to find the Curved Surface Area :
\tt C.S.A = 2\pi rhC.S.A=2πrh
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✰ The height of the cylinder is 2cm
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→ We know that,
⠀⠀⠀» Circumference of the base = 5cm
⠀⠀⠀» C.S.A of the cylinder is 10cm²
~ Now let's find the radius of the cylinder with the help of the formula mention below...
⋆ Formula,
→ Circumference = 2πr
~ Now let's find the radius of the cylinder with the help of the circumference of the base given taking the value of π as 22/7...
\longrightarrow \tt Circumference = 2\pi r⟶Circumference=2πr
\longrightarrow \tt 5cm = 2 \times \dfrac{22}{7} \times r⟶5cm=2×722×r
\longrightarrow \tt r = \dfrac{5\times 7}{2 \times 22}⟶r=2×225×7
\longrightarrow \tt r = \dfrac{35}{44}⟶r=4435
Henceforth the radius of the cylinder is 35/44cm
~ Now let's find the height of the cylinder with the help of the formula mention below...
⋆ Formula,
→ C.S.A of the cylinder = 2πrh
~ Now let's find the height of the cylinder with the help of the C.S.A and the radius which we found taking the value of π as 22/7...
\longrightarrow \tt C.S.A = 2\pi rh⟶C.S.A=2πrh
\longrightarrow \tt 10 = 2 \times \dfrac{22}{7} \times \dfrac{35}{44} \times h⟶10=2×722×4435×h
\longrightarrow \tt h = \dfrac{\cancel{10}\times \cancel{44} \times \cancel{ 7}}{\cancel{35}\times \cancel{ 22 }\times \cancel{ 2}}⟶h=35×22×210×44×7
\longrightarrow \tt h = 2⟶h=2
Henceforth the height of the cylinder is 2cm
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⋆ Related Formulas,
\;\;\;\;\;\;\; \leadsto \tt volume\; of \; a \; cylinder = \pi r^{2} h⇝volumeofacylinder=πr2h
\;\;\;\;\;\;\;{ \leadsto} \tt T.S.A \; of \; a \; cylinder= 2\pi rh + 2\pi r^{2}⇝T.S.Aofacylinder=2πrh+2πr2
\;\;\;\;\;\;\; \leadsto \tt Volume \; a \; cube = Side ^3⇝Volumeacube=Side3
\;\;\;\;\;\;\; \leadsto \tt L.S.A \; of \; a \; cube = 4(L)^{2}⇝L.S.Aofacube=4(L)2
\;\;\;\;\;\;\; \leadsto \tt T.S.A \; of \; a \; cube = 6(L)^{2}⇝T.S.Aofacube=6(L)2
⋆ 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{35/44cm}}\put(9,17.5){\sf{2cm}}\end{picture}
* Note : View the diagram from the web if difficulty in seeing from the app
See this question at : https://brainly.in/question/40343207