Question

2. The curved surface area of the cylinder is 900
cm. If the circumference of the base and its
height are equal then the height of the cylinder is​

Answer 1

it is given that curved surface area of the cylinder is 900 cm².

if the circumference of the base and its height are equal then we have to find height of the cylinder.

we know, curved surface area of cylinder = 2πrh

⇒900 = 2π rh

⇒πrh = 450 .........(1)

circumference of base = height

⇒2πr = h

⇒r = h/2π ........(2)

putting equation (2) in equation (1) we get,

π (h/2π)h = 450

⇒h² = 900

⇒h = 30 cm

therefore, the height of the cylinder is 30cm.

Answer 2

$Let \: p \:and \: h \: are \: Circumference \\and \: Height \: of \:a \: Cylinder \: respectively$

$\blue {p = h}\:---(1) \: (given)$

$\boxed { \pink { CSA \: of \:a \: cylinder= p \times h }}$

$\implies CSA = 900\: cm^{2} \: (given)$

$\implies p\times h = 900$

$\implies h \times h = 900\:[From \: (1) ]$

$\implies h^{2} = (30\: cm)^{2}$

$\implies h = \sqrt{(30\:cm)^{2}}$

$\implies h = 30 \:cm$

Therefore.,

$\red { Height \: of \: of \:the \: Cylinder } \green { = 30 \:cm}$

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