Question

1. The total surface area of a cylinder is 924 cm?. If its radius of the base is 7 cm, find its
height and volume.answer is 14cm and 2156cm3 explain it​

Answer 1

Answer:

This is the answer of your problem

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Answer 2

${ \large{ \underline{ \pmb{ \sf{Given... }}}}}$

★The total surface area of a cylinder is 924cm²

★The radius of the base is 7cm

${ \large{ \underline{ \pmb{ \sf{To \: Find... }}}}}$

★ The hieght and the volume of the cylinder.

${ \large{ \underline{ \pmb{ \sf{Solution... }}}}}$

➼ The hieght and the volume of the cylinder are 14cm and 2156cm³ respectively.

${ \large{ \underline{ \pmb{ \sf{Full \: Solution ... }}}}}$

~ Now let's find the hieght of the cylinder to find the volume of it.

★Formula:

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

~ Now as we know that the T.S.A = 924cm² and radius is 7cm let's substitute the values and find the hieght

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

${ : \implies} \sf 924 {cm}^{2} = 2 \times \dfrac{22}{7} \times 7(7 + h)$

${ : \implies} \sf 7 + h = \dfrac{924 \times 7}{2 \times 22 \times 7}$

${ : \implies} \sf 7 + h = 21 cm$

${ : \implies} \sf { \boxed{ \pmb{ \frak{h = 14cm}}}}$

• Henceforth the hieght of the cylinder is 14cm

~ Now let's find the volume of the cylinder

★ Formula:

$\bigstar{ \boxed{ \sf{Volume \:of \: cylinder = \pi {r}^{2} h}}}$

~ As we know that the radius of the cylinder is 7 and hieght of the cylinder is 14cm let's find the value of its volume.

${ : \implies} \sf Volume = \pi {r}^{2} h$

${ : \implies} \sf Volume = \dfrac{22}{7} \times {7}^{2} \times 14$

${ : \implies} \sf Volume = 22 \times 7 \times 14$

${ : \implies} \sf Volume = { \boxed{ \pmb{ \frak{2156 {cm}^{3} }}} \bigstar}$

• Henceforth the volume of the cylinder is 2156cm³