Question

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.

Answer 1

Question:-

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.

Required Answer:-

Given:-

$\\ \sf{ \rightarrow{Sum \: of \: the \: radius \: of \: radius \: and \: height \: is \: 37cm}}$

$\sf{ \rightarrow{Total \: surface \: area \: of \: the \: cylinder \: is \: 1628sq.cm.}}$

To Find:-

$\\ \sf{ \rightarrow{Volume \: of \: the \: cylinder}}$

♡Solution:-

Here, we are given, sum of the radius (r) and height (h) is 37cm

$\\ \therefore{ \bold{r + h} = \sf{37cm}}$

Again, total surface area of the right circular cylinder is 1628sq.cm.

As we know that,

$\\ \sf{Total \: surface \: area \: of \: cylinder = 2\pi r(r + h) }$

According to the question,

$\\ \pmb{2\pi r(r + h) = 1628}$

$\\ \sf{ \implies{2\pi r \times 37 = 1628}} \: \: \: \: \: \: \: \: \boxed{ \rm{ \because{(r + h) = 37}}}$

$\\ \sf{ \implies{2\pi r = \frac{1628}{37} }}$

$\\ \sf{ \implies{r = \frac{1628}{37 \times 2 \times \frac{22}{7} } }}$

$\\ \sf{ \therefore{ \bold{r = 7}}}$

Hence,

$\\ \sf{ \pmb{r + h = 37}}$

$\\ \sf{ \implies{7 + h = 37}}$

$\\ \sf{ \implies{h = 37 - 7}}$

$\\ \sf{ \therefore{ \bold{h = 30}}}$

$\\ \rm{ Hence \: radius \: of \: the \: cylinder \: is \: \bold{7cm} \: and \: the \: height \: is \: \bold{30cm}}$

Now, we know that,

$\\ \underline{ \boxed{ \pmb{ \blue{Volume \: of \: cylinder = \pi {r}^{2} h}}}}$

Therefore,

$\\ \sf{Volume \: of \: the \: cylinder = \bold{ \frac{22}{7} \times {(7cm)}^{2} \times 30cm}}$

$\\ \sf{ \implies{Volume \: of \: the \: cylinder = \bold{( \frac{22}{7} \times {7}^{2} \times 30) {cm}^{3} }}}$

$\\ \sf{ \therefore{Volume \: of \: the \: cylinder = \bold{ \red{4620cm {}^{3} }}}}$

$\\ \underline{ \boxed{ \rm{ \green{Hence, \: the \: volume \: of \: the \: cylinder \: is \: \bold{4620cm {}^{3} }}}}}$

Answer 2

$\huge\bf{Question:-}$

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.

$\huge\bf{Solution:-}$

(Refer to attachment)

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