Question

If the curved surface area of a right circular cylinder whose base radius and height are equal is 72piecm^2, then the diameter of the base is.​

Answer 1

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Radius of cylinder (r)=7cm

Height of cylinder (h)=15cm

Curved Surface Area =2πrh

=2×(22/7)×7×15

=660cm

2

Total Surface Area =2πr(h+r)

=2×(22/7)×7(15+7)

=2×22×22

=968cm

Answer 2

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Solution :-

We know,

Curved surface area of cylinder = 2πrh

[Where, r is radius and h is height of cylinder]

Put all values :

$\longrightarrow 72π = 2 × π × r × h$

Radius and height are equal.

$\longrightarrow 72π = 2π × r × r$

$\longrightarrow 72π = 2π × r²$

$\sf \longrightarrow \dfrac{72 \: \cancel{\pi}}{2 \: \cancel{\pi}}$

$\longrightarrow 36 = r²$

$\longrightarrow √36 = r$

$\longrightarrow \: r = 6$

Radius of cylinder is 6 cm.

Now,

• Diameter = 2 × radius

$⟶ Diameter = 2 × 6$

$\longrightarrow \: Diameter = 12$

Therefore,

• Diameter of base of cylinder is 12 cm.