Question

13. Joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm
Find the area of shape required to make 10 such caps.​

Answer 1

Given:

• Joker's cap is in the form of a right circular cone.
• Radius = 7cm.
• Height = 24cm.

To find:

• The area of shape required to make 10 such caps.

Solution:

• Let's consider radius & height as r & h.

Where,

• Radius = 7cm
• Height = 24cm

• Let's consider slant height as l

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Finding surface area of the cone,

→ l² = r² + h²

→ l² = (7)² + (24)²

→ l² = 49 + 576

→ l² = 625

→ l = √625

→ l = 25cm

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Let's Find curved surface area,

We know that,

→ πrl

→ 22/7 × 7 × 25

→ 22 × 25

→ 550cm²

∴ Hence, If Curved surface area of 1 cap is 550 m², 5500m² will be the curved surface area of 10 caps.

Answer 2

Answer :-

• Area of the shape required for making 10 conical caps = 550 cm².

Step by step explanation :-

Given :-

1. The cap is in the form of a cone.
2. Base radius of the cone = 7 cm.
3. Height of the cone = 24 cm.
4. Number of caps to be made = 10 Caps.

To find :-

• Area required for the making of 10 caps.

Concept :-

• Finding the slant height of the cap with the help of radius and height.

• Solving the curved surface for finding the area of 1 cap.

• Multiplying the area of 1 cap with 10 for finding area of 10 similar conical caps.

Solution :-

As we have given with the base radius and the height, we'll find out the slant height by using the formula :-

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

Where,

1. l = slant height ( to be find ).
2. r = base radius.
3. h = height of the cap.

Putting the values ,

l = √(24)²+(7)²

⇒ √576+49

⇒ √625 = 25 cm.

Since, we've all the necessary dimensions, we'll find the curved surface area of 1 cap.

By applying the formula :-

☆ π×r×l

⇒ 22/7 × 25 × 7

⇒ 22×25 = 550 cm².

Now, finding the area of 10 similar caps :-

area of 10 caps = area of 1 cap × 10

⇒ 550×10 = 5500 cm².