Question

The csa of a right circular cylinder iss 2288 cm2 and the circumfenceis 88 cm find the height and tsa of the cyclinder

Answer 1

• The height of the cylinder = 26 cm.
• The total surface area (T.S.A.) of the cylinder = 3520 cm².

Given :

• The curved surface area (C.S.A.) = 2288 cm².
• The circumference = 88 cm.

To Find :

• The height of a right circular cylinder.
• The total surface area (T.S.A.) of the cylinder.

Solution :

1) The height of the cylinder.

Given,

Cirumference = 88 cm

$: \implies \rm2\pi r = 88 \: cm$

Also given,

C.S.A. of the cylinder = 2288 cm²

$: \implies \rm2\pi rh = 2288 \: {cm}^{2}$

Substitute the given value of the circumference in the formula of curved surface area (C.S.A.) of the cylinder.

$: \implies \rm88 \: cm \times h = 2288 \: {cm}^{2} \\ \\ : \implies \rm h = \cancel\dfrac{2288 \: {cm}^{2} } {88 \: cm} \\ \\ : \implies \rm h = \cancel\dfrac{1144}{44} \: cm \\ \\ : \implies \rm h = \cancel\dfrac{572}{22} \: cm \\ \\ : \implies \rm h = \cancel\dfrac{286}{11} \: cm \\ \\ : \implies \rm h = 26 \: cm$

Hence,

The height of a right circular cylinder is 26 cm.

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2) The total surface area (T.S.A.) of the cylinder.

We know that,

$\blue{ \boxed{ \red{ \sf{T.S.A. \: Of \: The \: Cylinder = 2\pi r(r +h )}}}}$

We need to find the radius (r) of the cylinder.

Given,

• The circumference = 88 cm

$: \implies \rm2\pi r = 88 \: cm \\ \\ : \implies \rm2 \times \dfrac{22}{7} \times r = 88 \: cm \\ \\ : \implies \rm\dfrac{22}{7} \times r = \cancel \dfrac{88}{2} \: cm \\ \\ : \implies \rm\dfrac{22}{7} \times r = 44 \: cm \\ \\ : \implies \rm r = 44 \: cm\times \frac{7}{22} \\ \\ : \implies r = 2 \: cm \times 7 \\ \\ : \implies r = 14 \: cm$

Hence, the radius (r) of the cylinder is 14 cm.

Substitute the given value of circumference in the formula of the total surface area (T.S.A.) of the cylinder.

$: \implies \rm 2\pi r \: (r + h) \\ \\ : \implies \rm88 \: cm \: (14 \: cm + 26 \: cm) \\ \\ : \implies \rm 88 \: cm \: (40 \: cm) \\ \\ : \implies \rm 88 \: cm \times 40 \: cm \\ \\ : \implies \rm3520 \: {cm}^{2}$

Hence,

The total surface area (T.S.A.) of the cylinder is 3520 cm².