Question

a solid is in the form of a right circular cylinder with a hemisphere shape at one end and a cone at the other end. their common diameter is 4.2 cm and heights of the cylindrical and conical portion are 12 cm and 7cm. respectively find the volume of the solid toy (π = 22/7)​

Answer 1

Given

• A Solid toy made up of right circular cylinder and hemisphere shape and cone.
• Diameter of the solid toy = 4.2cm
• Height of cylinder = 12cm
• Height of cone = 7cm

To Find

• Find the volume of the solid toy ?

Formula used

• Volume of cone = ⅓πr²h
• volume of cylinder = πr²h
• volume of hemisphere = ⅔πr³

Solution

Diameter of right circular cylinder and hemisphere shape and cone is 4.2cm

Radius = 4.2/2= 2.1cm

$\huge{\pink{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~}}}$

Height of cylinder = 12cm

Radius of Cylinder= 2.1cm

volume of cylinder = ?

We know

volume of cylinder = πr²h

• Putting the values

${volume \: of \: cylinder = \frac{22}{7} \times {2.1}^{2} \times 12}$

${volume \: of \: cylinder = \frac{22}{7} \times 4.41 \times 12}$

${volume \: of \: cylinder = \dfrac{1164.24}{7}}$

$\bf\orange{volume \: of \: cylinder = 166.32}$

$\huge{\pink{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~}}}$

Height of cone = 7cm

Radius of cone= 2.1cm

Volume of cone = ?

we know that,

$Volume \: of \: cone = \frac{1}{3} πr²h$

${Volume \: of \: cone = \frac{1}{3} \times \frac{22}{7} \times {2.1}^{2} \times 7}$

${Volume \: of \: cone = \frac{1}{3} \times {22} \times 4.41 }$

${Volume \: of \: cone = \frac{97.02}{3} }$

$\bf\green{Volume \: of \: cone = 32.34 }$

$\huge{\pink{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~}}}$

Radius of Hemisphere 2.1cm

volume of Hemisphere = ?

we know that,

${volume \: of \: hemisphere = \frac{2}{3} \times \frac{22}{7} \times {r}^{3} }$

${volume \: of \: hemisphere = \frac{2}{3} \times \frac{22}{7} \times {2.1}^{3} }$

${volume \: of \: hemisphere = \frac{44}{21} \times 9.261 }$

${volume \: of \: hemisphere = \frac{407.484}{21} }$

$\bf\red{volume \: of \: hemisphere = 19.404 }$

$\huge{\pink{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~}}}$

$\\ \\ \bf {Volume~ of ~~the~~ solid ~~toy = \sf{volume \: of \: cylinder + Volume \: of \: cone +volume \: of \: hemisphere}}$

$\bf {Volume~ of ~~the~~ solid ~~toy = \sf 166.32 +32.34 + 19.404}$

$\bf {Volume~ of ~~the~~ solid ~~toy = 218.064}$

$\: \: \: \: \: \: \: \: \gray{\underline{\bf{volume \: of \: the \: solid \: toy = 218.064cm²}}}$

Answer 2

volume of solid toy = 218 cm³