Math, asked by adiveer134, 6 months ago

the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm 2 is

Answers

Answered by brainlyofficial11
100

Aɴsʀ

given :-

  • radius of cylinder, r = 7cm
  • total surface area of cylinder = 968 cm²

to find :-

  • height of cylinder ?

solution :-

we know that,

  • T.S.A = total surface area
  • r = radius of cylinder
  • h = height of cylinder

 \boxed{\bold \red{ T.S.A\: of \: cylinder = 2 \pi  r(r + h)}} \\

and it is given that

  • total surface of cylinder = 968 cm²
  • and radius of cylinder, r = 7cm

 \bold{ \implies 968 \:   = 2 \times  \frac{22}{ \cancel{7}}  \times  \cancel{7}(7 + h)} \\  \\  \bold{ \implies 968 =44 \times (7 + h)  } \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\   \bold{ \implies 7 + h =   \cancel{\frac{968}{44}} } \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:   \:  \:  \:  \:  \:  \:  \:  \\  \\  \bold{ \implies 7 + h = 22} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \\  \\  \bold{ \implies \: h = 22 - 7  } \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\    \implies \boxed{\bold \orange{h = 15 \: cm}} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:

therefore, height of the cylinder is 15 cm

_______________________

additional information :-

if r and h denote respectively the radius of the base and height of a right circular cylinder then,

  • Area of each end = πr² sq.units

  • Curved surface area = 2πrh sq.units

  • Total surface area = 2πr(r+h) sq.units

  • volume = πr²h = (area of the base× height) cu.units
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