Question

the thickness of a hollow metallic cylinder is 2 centimetre it is 35 cm long and its inner radius 12 cm find the volume of metal required to make the cylinder assuming it's open at either end

Answer 1

Answer:

$\huge \bold{5720 {cm}^{3} }$

Step-by-step explanation:

$\blue{ \sf{ \underline{ \pink{ \underline{ \purple{given}}}}}}$

thickness of hollow cylinder is 2 cm

length=35cm

Inner radius=12cm

outer radius=12+2=14cm

$\huge \orange{ \fbox{ \fbox{ \red{ \mathfrak{solution}}}}}$

volume volume of wood required to make the cylinder = volume of whole cylinder - volume of hollow cylinder.

$\pi \times {r}^{2} \times h - \pi \times {r}^{2} \times h$

$= \: \: \pi( {r}^{2} - {r}^{2} )h$

$= \frac{22}{7} ( {14}^{2} - {12}^{2} )35$

$= \frac{22}{7} (196 - 144)35$

$= \frac{22}{ \cancel7} \times 52 \times \cancel35$

$= 22 \times 52 \times 5$

$= 5720 {cm}^{3}$

$\bf{hope \: this \: helps \: you }$

Answer 2

$\large{\underline{\sf{\red{Required\:Answer:}}}}$

• $\large\boxed{\underline{{\sf {5720 \: cm}^{2}}}}$

Given:-

• Inner radius of cylinder r = 12 cm.

• Thickness = 2 cm.

• Height = 35 cm.

To Find:-

• Other radius.

• Volume of metal required to make cylinder.

Solution:-

• Other radius R = ${\sf{12 + 2 = 14 \: cm }}$

• It is a hollow cylinder.

$\large\boxed{\underline{\pink{\sf Volume \: of \: metal \: required \: to \: make \: cylinder = outer \: volume - inner \: volume}}}$

$\purple{\implies\:\:}$ ${\sf{ \pi R^{2} h - \pi r ^{2} h }}$

$\purple{\implies\:\:}$ ${\sf{\dfrac{22}{7} \times 35 \times (14 ^{2} - 12 ^{2}) }}$

$\purple{\implies\:\:}$ ${\sf{{5720 \: cm}^{2} }}$

✤ Hence, the volume of metal required to make the cylinder, assuming it is open, at either end = ${\sf{ {5720 \: cm}^{2} }}$