Question

find the height and LSA of a cylinder if it's redius is 28 and TSA is 5805m^2​

Answer 1

Given :-

● Total surface area of cylindrical = 5805m^2

● Radius of the cylinder = 28m

Solution :-

Here ,

Radius of the cylinder = 28m

TSA of cylinder = 5805m^2

The value of π = 22/7

As we know that,

TSA of cylinder = 2πr( r + h)

Put the required values in the given formula,

5805 = 2 * 22/7 * 28 ( 28 + h )

5805 = 2 * 22 * 4 ( 28 + h )

5805 = 44 * 4 * ( 28 + h )

5805 = 176 ( 28 + h )

5805 = 4928 + 176 h

5805 - 4928 = 176h

877 = 176h

h = 4.98m

[you can take approx value also that is 5]

Now,

LSA of Cylinder = 2πrh

Put the required values in the formula ,

LSA of Cylinder = 2 * 22/7 * 28 * 4.98

LSA of Cylinder = 2 * 22 * 4 * 4.98

LSA of Cylinder = 44 * 4 * 4.98

LSA of Cylinder = 176 * 4.98

LSA of Cylinder = 876.48m^2

Hence, The Lateral surface area of cylinder is 876.48m^2 $.$

Answer 2

★ Given :-

• ❍ Radius of the cylinder = 28m

• ❍ T.S.A of cylinder = 5805m²

★ To Find :-

• ❍ The height and L.S.A of a cylinder.

★ Solution :-

❒ As we know that ,

• ❍ The value of π = 22/7

• ❍ T.S.A of cylinder = 2πr( r + h)

☯ Then,

➙ 5805 = 2 * 22/7 * 28 ( 28 + h )

➙ 5805 = 2 * 22 * 4 ( 28 + h )

➙ 5805 = 44 * 4 * ( 28 + h )

➙ 5805 = 176 ( 28 + h )

➙ 5805 = 4928 + 176 h

➙ 5805 - 4928 = 176h

➙ 877 = 176h

➙ h = 4.98m. ★

( approximately the value is 5 )

❒ As we know that,

• ❍ LSA of Cylinder = 2πrh

☯ Then,

➙ LSA of Cylinder = 2 * 22/7 * 28 * 4.98

➙ LSA of Cylinder = 2 * 22 * 4 * 4.98

➙ LSA of Cylinder = 44 * 4 * 4.98

➙ LSA of Cylinder = 176 * 4.98

➙ LSA of Cylinder = 876.48m^2

Therefore,

The L.S.A of cylinder = 876.48m² .

★ Hope it helps u ★