Question

if the curved surface area of a cylinder is numerically equal to its volume then the diameter of its base is what

Answer 1

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For a cylinder of base radius r and height h ,

lateral surface area or curved surface area ,

is given by .....

$\implies \boxed{L.S.A. = 2\pi rh}$

.and volume is given by..

$\implies \boxed{volume = \pi r {}^{2} h}$

•now according to the Question..

curved surface area of a cylinder is numerically equal to its volume..

therefore....

$\implies \: 2\pi rh = \pi r {}^{2} h \\ \implies \: 2 = r \\ \implies \: r = 2 \: \\ \implies \: d = 2r \: = 2 \times 2 \\ \implies \: d = 4 \: unit$

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Answer 2

Answer:

Diameter=4

Step-by-step explanation:

$csa = 2\pi \: rh \\ volume = \pi {r}^{2}h \\ 2\pi \: rh = \pi {r}^{2} h \\ r = 2 \\ d = 2r \\ d = 4$