Question

16. The sum of the radius and height of a cylinder is 37 cm and the total surface area of
the cylinder is 1628 cm Find the height and the volume of the cylinder
​

Answer 1

Answer:

Given r+h=37 cm

Total surface area of the solid cylinder = 2πr(r+h)=1628cm

2

∴r=

2×22×37

1628×7

=7cm

∴ Height = (37-7) cn = 30 cm

and Circumference = 2πr=

7

22

×7=44cm

Volume of the cylinder = πr

2

h=

7

22

×7×7×30=4620cm

3

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 16. \: The \: sum \: of \: the \: radius \: and \: height \: of \: a \: cylinder\\\tt is \: 37 \: cm \: and \: the \: total \: surface \: area \: of \: the\\\tt cylinder \: is \: 1628 \: {cm}^{2} Find \: the \: height \: and\\\tt the \: volume \: of \: the \: cylinder.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf Sum\:of \:the \:radius \:and\:height (r+h) = 37\:cm$
• $\sf \bf Total\:surface \:area \:of \:cylinder (TSA) = 1628\:{cm}^{2}$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf Height \:of\:the \:cylinder$
• $\sf \bf Volume \:of\:the \:cylinder$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\color {springgreen}\underline {\sf (i) Height \:of\:the \:cylinder}}$

${\boxed {\boxed {\boxed {\color {blue} {\sf \bf TSA=2 \pi r \Big(r+h\Big)}}}}}$

• $\sf TSA=total \:surface \:area \:of \:cylinder$
• $\sf r=radius \:of\:the \:cylinder$
• $\sf h=height \:of\:the \:cylinder$

${\overbrace {\underbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

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

$\sf \bf \implies 1628=74 \times \dfrac{22}{7} \times r$

$\sf \bf \implies 1628=\dfrac{1628}{7}\times r$

$\sf \bf \implies r=1628 \times \dfrac{7}{1628}$

$\sf \bf \implies r=\cancel{1628} \times \dfrac{7}{\cancel {1628}}$

$\implies {\boxed {\boxed{\color {green} {\sf \bf r=7\:cm}}}}$

-------------------------------------------------------

$\sf \bf \implies \Big(r+h\Big) =37 \longrightarrow \big(Given \big)$

${\overbrace {\underbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies 7+h=37$

$\sf \bf \implies h=37-7$

$\implies {\boxed {\boxed {\color {aqua} {\sf \bf h=30\:cm}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\sf \therefore The\:height \:of\:the \:cylinder \:is\:30\:cm}}}}}$

———————————————————————————

${\color {springgreen}\underline {\sf (i) Volume \:of\:the \:cylinder}}$

${\boxed {\boxed {\boxed {\color {blue} {\sf \bf V= \pi {r}^{2}h}}}}}$

• $\sf V=Volume \:of \:cylinder$
• $\sf r=radius \:of\:the \:cylinder$
• $\sf h=height \:of\:the \:cylinder$

${\overbrace {\underbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies V=\dfrac{22}{7} \times {\Big(7\Big)}^{2} \times 30$

$\sf \bf \implies V=\dfrac{22}{7} \times 7 \times 7 \times 30$

$\sf \bf \implies V=\dfrac{22}{\cancel {7}} \times \cancel {7} \times 7 \times 30$

$\sf \bf \implies 22 \times 7 \times 30$

$\implies {\boxed {\boxed {\color {aqua} {\sf \bf V=4620\:{cm}^{3}}}}}$

${\underbrace {\color {red} {\underline {\color {red} {\sf \therefore The\:volume \:of\:the \:cylinder \:is\:4620\:{cm}^{3}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\bf Lateral \:surface \:area \:of \:cylinder = 2 \pi r h$

$\bf Total \:surface \:area \:of \:cylinder =2 \pi r \Big(r+h\Big)$

$\bf Volume \:of\:cylinder = \pi {r}^{2} h$