Question

A joker's cap is in the form of a right circular cone whose base radius is 7 cm and height is 24 cm. Find the area of the sheet required to make 10 such caps.

Answer 1

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.8cm}\begin{picture}(16,4)\thicklines\put(8,1){\line(1,0){1}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.03,1.8){\sf{24 cm}}\put(9,1){\line(0,2){2}}\put(8.4,0.83){\sf{7 cm}}\qbezier(8,1)(9,1.5)(10,1)\qbezier(8,1)(9,0.4)(10,1)\end{picture}$

$\rule{160}{1}$

• As we have to make a Joker Cap, so it will be Open from Bottom.
• We Just Need to Make CSA of Cone.

$\underline{\bigstar\:\:\textsf{Area of Sheet Required for 10 Caps :}}$

$\dashrightarrow\tt\:\:Area=CSA_{cone} \times Number_{cap}\\\\\\\dashrightarrow\tt\:\:Area=(\pi rl) \times 10\\\\\\\dashrightarrow\tt\:\:Area = \pi r \sqrt{ {r}^{2} + {h}^{2} } \times 10\\\\\\\dashrightarrow\tt\:\:Area = \dfrac{22}{7} \times 7 \times \sqrt{{(7)}^{2} + {(24)}^{2}} \times 10\\\\\\\dashrightarrow\tt\:\:Area = 22 \times \sqrt{49 + 576} \times 10\\\\\\\dashrightarrow\tt\:\:Area = 22 \times \sqrt{625} \times 10\\\\\\\dashrightarrow\tt\:\:Area = 22 \times 25 \times 10\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{\textbf{Area = 5,500 cm ^\textbf2 }}}}$

⠀

$\therefore\:\underline{\textsf{Area of sheet required for caps is \textbf{5,500 cm ^\textbf2 }}}$

Answer 2

AnswEr:-

Area of sheet required for making 10 such caps = 5500 cm²

$\rule{200}{1}$

Here,given :-

☛ Radius (r) = 7 cm

☛ Height (h) = 24 cm

To find out:-

☛ Area of sheet required to make 10 such caps = ?

Solution:-

As here area of sheet required to make a cap, then here cap will be open from bottom.So we don't need to find TSA of cone,we need to find curved surface area of cone will be required.

We know,

☛ CSA of cone = πrl

Here,r = radius of cone.

And,l = slant height of cone.

First we need to find slant height.

We also know,

☛ Slant height (l) = √(r² + h²)

⇒ Slant height (l) = √(7² + 24²)

⇒ Slant height (l) = √(49 + 576)

⇒ Slant height (l) = √625

⇒ Slant height (l) = 25 cm

Now putting values in formula for CSA of cone:-

⇒ CSA of cone = 22/7 × 7 × 25

⇒ CSA of cone = 22 × 25

⇒ CSA of one cone = 550 cm²

∴ Area of sheet required to make 1 cap = 550 cm²

Now finding area of sheet required to make such 10 caps:-

⇒ Area of sheet required = (550 × 10)

⇒ Area of sheet required = 5500 cm²

Therefore,

Area of sheet required to make such 10 caps = 5500 cm² .