Question

Conical caps are designed for a birthday party. If the radius of the base is 8 cm and height of each cap is 6 cm, then how many cm2 of material is needed for 21 caps?
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Answer 1

Answer:

according to question we have to find CSA of conical caps as they are 21

22/7 r(l+r).

as l = root r square -h square.

as l=root 64-36

as l= root 28

as l =2root7

by putting it in formula 22/7 8+(2root7+8) ×21

66×8(2root7)

528(2root7) cm material is needed.

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Answer 2

Answer:

Area of material required for 21 caps is 5257.2 cm² .

Step-by-step explanation:

Given that :

• Radius of base of cone = 8 cm
• Height of conical cap = 6 cm

To find :

• Area of material needed for 21 caps

Solution :

• The area of material required for 1 conical cap = lateral surface area of cap.
• Lateral surface area of cap is given by :
• Lateral Surface Area = πrl
• where, l is slant height of cone.
• The slant height, base radius and height of cone form a right angled triangle. The right angle is between base radius and height of cone.
• By Pythagoras theorem,

$l = \sqrt{ {r}^{2} + {h}^{2} }$

• Hence, lateral surface area of cone becomes

$Lateral \: Surface \: Area = \pi \: r \sqrt{ {r}^{2} + {h}^{2} }$

• Putting values in above equation, we get;

$Lateral \: Surface \: Area = \pi \times 8 \times \sqrt{ {(8)}^{2} + {(6)}^{2} } \\ = 3.14 \times 8 \times \sqrt{64 + 36} \\ = 3.14 \times 8 \times \sqrt{100} \\ = 3.14 \times 8 \times 10 \\ = 251.2 \: {cm}^{2}$

• Area of material required for one cap is 251.2 cm².
• Area of material required for 21 caps is (251.2 x 21) cm² = 5275.2 cm².
• Hence, area of material required for 21 caps is 5257.2 cm² .