Question

a joker cap is in the form of the right circular cone of base radius 7 cm and height 24 cm . find the area of sheet required for making 10 sach caps​

Answer 1

Step-by-step explanation:

first find the lateral height (l) by applying Pythagoras theorem.

then required area =. 10.π.r.l

Answer 2

$\bigstar\: \large\underline{\red{\sf{ \: \: \: \: \: Given : \: \: \: \: }}}$

• Radius of right circular cone = 7 cm
• Height of right circular cone = 24 cm

$\bigstar\: \large\underline{\red{\sf{ \: \: \: \: \: To \:Find : \: \: \: \: }}}$

• The area of sheet required for making 10 such caps.

$\bigstar\: \large\underline{\red{\sf{ \: \: \: \: \: Solution:\: \: \: \: }}}$

$\purple{\qquad\qquad\tiny \dag \: \: \underline\frak{Slant \: Height \: of \: the \: cone:} }$

$:\implies\sf (Slant \: Height)^2 = (Radius)^2 + (Height)^2$

$:\implies\sf (Slant \: Height)^2 = (7)^2 + (24)^2$

$:\implies\sf (Slant \: Height)^2 =49 + 576$

$:\implies\sf (Slant \: Height)^2 =625$

$:\implies\sf Slant \: Height = \sqrt{625}$

$:\implies\underline{ \boxed{\sf Slant \: Height = 25 \: cm}}$

_______________________________

$\tiny\orange{\qquad\qquad\qquad\dag \: \: \underline\frak{Curved \: Surface \: Area\: of \:cone:} }$

$\dashrightarrow\:\:\sf CSA \: of \: cone =\pi rl$

$\dashrightarrow\:\:\sf CSA \: of \: cone = \dfrac{22}{7} \times 7 \times 25$

$\dashrightarrow\:\:\sf CSA \: of \: cone = 22 \times 25$

$\dashrightarrow\:\: \underline{\boxed{\sf CSA \: of \: cone = 550 \: {cm}^{2}}}$

______________________________

$\tiny\pink{\qquad\qquad\qquad\dag \: \: \underline\frak{Total \: Sheet \: required\: to \:make\:10\: such\:caps:} }$

$:\implies \sf 10 \times CSA \: of \: cone$

$:\implies \sf 10 \times550$

$:\implies \underline{\boxed{ \textsf{\textbf{5500 {cm} ^{\text 2} }}}}$

$\therefore\:\:\underline{\textsf{The area of sheet required for making 10 such caps is \textbf{5500 cm ^{ \text 2} }}}.$