Question

Find the total surface area of cylinder height 7 cm area of a circle is 250 cm sq

Answer 1

Answer

• Total Surface Area of the cylinder is 905.1 cm²

Explanation

Given

• Height of the cylinder is 7 cm
• Area of the base is 250 cm²

To Find

• Total Surface Area of the cylinder?

Solition

[We shall first find the radius of the the base of the cylinder and then simply substituting them on formula will get us our Answer]

✭ Radius of the cylinder

➝ Area of circle = πr²

• Area = 250 cm²

➝ 250 = πr²

➝ 250 = 22/7 × r²

➝ 250 × 7/22 = r²

➝ 79.5 = r²

➝ √79.5 = r

➝ Radius = 9 cm

✭ TSA of cylinder

➝ TSA of cylinder = 2πr(h+r)

➝ TSA = 2 × 22/7 × 9 (7+9)

➝ TSA = 44/7 × 9(16)

➝ TSA = 44/7 × 144

➝ TSA = 905.1 cm²

Answer 2

Given

• Height of cylinder = 7cm
• Area of circle = 250cm²

To find

• Total surface of the cylinder.

Figure

$\setlength{\unitlength}{1.4cm} \thicklines \begin{picture}(0,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(1,1){\line(0,1){1}}\put(1,1){\line(0, - 1){1}}\put(1.1,1.1){ \bf\large 7cm }\put(1.2,-0.3){ \bf\large r }\put(1,0){\line(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\end{picture}$

Solution

★ First of all we have to calculate the radius of the circle.

$\underline{\boxed{Area\: of\: a\: circle = πr^2}}$

→ Area of circle = 22/7 × r²

→ 250 = 22/7 × r²

→ r² = 79.5

→ r = √79.5 cm

→ radius = 9 cm

Now,

$\underline{\boxed{T.S.A\: of\: a\: cylinder = 2πr(h + r)}}$

→ T.S.A of cylinder = 2 × 22/7 × 9 (7 + 9)

→ T.S.A of cylinder = 44/7 × 9 (16)

→ T.S.A of cylinder = 44/7 × 144

→ T.S.A of cylinder = 6336/7

→ T.S.A of cylinder = 905.14 cm²

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