Question

: A solid toy is in the form of a hemisphere surmounted by a right

circular cone. The height of the cone is 4 cm and the diameter of the base is 8 cm.

Determine the volume of the toy. If a cube circumscribes the toy, then find the differ-

ence of the volumes of cube and the toy. Also, find the total surface area of the toy.​

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Answer}}}}}$

$\textbf{height of cone}$$\sf\color{red}=\: 4\:cm$

$\textbf{now volume of toy = volume of cone + volume of hemis phere}$

$\textbf{so total volume =}$$\sf\color{red}2/3\: π r3 \:+\: 1/3\: π r2 h$

$\sf = π r2 ( 2/3 r + 1/3 h )$

$\sf= 22/7 × 4×4 (2/3 × 4 +1/3×4)$

$\sf = 22/7 × 16 (8/3 +4/3)$

$\sf = 22/7× 16 ×4 = 22/7 ×64 cube cm$

${ \large{ \boxed{ \red{ \underline{ \bf \:Curbed\: surface\: area \:of \:cone =}}}}}$

$\bold{\boxed{ π r l =π 4 √ (h2 +r2 )}}$

$\sf =π ×4 √(16+16)$

$\sf = π4√ 32$

$\sf =22/7 × 16√2$

$\textbf{surface area of toy}$ $\sf\color{red}=\:2π r2 \:+ πr.$

$\sf= 22/7 × 2× 16 + 22/7 ×16√2$

$\sf =22/7 ( 32 + 16√2)$

$\sf= 3.14× 54.56= 171.31 cm square' answer$

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Difference\: of \:volume\: of\: cube\: and \:toy}}}}}$

$\tt{answer}$ $\therefore\textbf{= 83 - 22/7 × 64 = 512 - 201 = 311 cube cm}$

Thankyou :)

You can also refer to the attachment :)

Answer 2

$\huge\bf{Solution:-}$

• (Refer to attachment)