Question

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The volume of a right circular cylinder is 1078 m³. If the area of its curved surface is equal to twice the area of the circular base, find the height of the cylinder. ​

Answer 1

Answer:

$h = 7 \: m$

Step-by-step explanation:

Gven:

$volume \: of \: a \: right \: circular \: cylinder = 1078 \: {m}^{3} . \\ curved \: surface \: area \: of \: right \: circular \: cylinder) = 2( area \: of \: the \: circular \: base)$

To Find

$height \: of \: the \: cylinder = h = ?$

Solution:

$(curved \: surface \: area \: of \: right \: circular \: cylinder) = 2( area \: of \: the \: circular \: base) \\ curved \: surface \: area \: of \: right \: circular \: cylinder) = 2\pirh \\ ( area \: of \: the \: circular \: base) = \pi{r}^{2} \\ \\ 2\pirh = 2(\pi {r}^{2}) \\ r = h \\ Now \\ volume \: of \: a \: right \: circular \: cylinder = 1078 \: {m}^{3} \\ volume \: of \: a \: right \: circular \: cylinder = \pi {r}^{2}h \\ as \: in \: this \: case \: r = h \\ volume \: of \: a \: right \: circular \: cylinder = \pi {h}^{3} \\ \pi {h}^{3} = 1078 \: {m}^{3} \\ h = {( \frac{1078}{\pi} )}^{( \frac{1}{3} )} \\ h = \sqrt[3]{343} \\ h = 7 \: m$