Question

Find the radius of the cylinder whose height is 15cm and the total surface area is
968 cm2.​

Answer 1

total surface area of cylinder= 2πr( h + r)

968 = 2×22/7 ×r( 15+ r )

968×7= 44r ( 15 +r )

6776 ÷ 44= r ( 15+ r)

154 = 15r + r2

r2 + 15r - 154 = 0

r2 + 22r -7r -154 = 0

r ( r + 22) -7 ( r + 22) = 0

( r + 22 ) ( r - 7 ) = 0

r + 22 =0. or r -7 =0.

r = -22 or 7

therefore ,radius of the cylinder is 7 cm

Answer 2

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Given :-

• Height ( h ) = 15 cm.

• Total surface area = 968 cm.

To Find :-

• The radius of the cylinder.

Solution :-

Formula used :-

» Total surface area ( TSA ) = 2πr(r+h)

Solving :-

» TSA = 2πr(r+h)

» 968 = 2 × 22/7 × r ( r + 15 )

» 968 × 7 = 44 × r ( r + 15 )

» 6776 ÷ 44 = r ( r + 15 )

» 154 = r² + 15r

» 154 - r² - 15r = 0

» 154- r² + 27r - 7r = 0

» r ( r + 22 ) - 7 ( r + 22 ) = 0

» ( r + 22 ) ( r - 7 ) = 0

» r + 22 = 0 or ( r - 7 ) = 0

» r = -22 or 7

Better to take 7 as the value of r .

Verification :-

» TSA = 2πr(r+h)

» 968 = 2×22/7 × 7 ( 7 + 15 )

» 968 = 2×22/7 × 7 ( 22 )

» 968 = 2×22/7 × 154

» 968 = 44/7 × 154

» 968 = 6.28( approx ) × 154

» 968 = 6.28 × 154

» 968 ≈ 967.12

Hence, verified !!!

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