Question

Find the curved surface area of a cone with base diameter 30cm and height 40cm

Answer 1

Given :-

• A cone with base diameter 30cm and height 40cm

To find :-

• Curved surface area of cone

Solution :-

• Diameter of cone = 30cm

• Radius of cone = 30/2 = 15cm

• Height of cone = 40cm

As we know that

→ slant height = √(height)² + (radius)²

→ l = √h² + r²

→ l = √(40)² + (15)²

→ l = √1600 + 225

→ l = √1825

→ l = 42.7 cm

Now,

Curved surface area of cone = πrl

Where " r " is radius and " l " is slant height of cone.

According to question

→ Curved surface area of cone

→ πrl

→ 22/7 × 15 × 42.7

→ 22 × 15 × 6.1

→ 330 × 6.1

→ 2013 cm²

Hence,

• Curved surface area of cone is 2013cm²

Extra Information :-

• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cylinder = πr²h
• Volume of cube = a³
• Volume of cone = ⅓ πr²h
• Volume of cuboid = l × b × h
• T.S.A of cube = 6a²
• C.S.A of cube = 4a²
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cuboid = 2(l + b)h

Answer 2

Answer :-

• Surface area of the cone is 2013cm².

Given :-

• A cone with base diameter 30cm and height 40cm.

To Find :-

• Curved surface area of the cone.

Solution :-

Here

• Diameter of the cone = 30cm => radius = 30/2 = 15cm
• Height of the cone = 40cm

As we know that

l = √h² + r²

Where

• l = slant height
• h = height
• r = radius

l = √ (40)² + (15)²

→ l = √ 1600 + 225

→ l = √ 1825

→ l = 42.7cm

As we know that

Curved surface area of a cone = πrl

According to question :-

22/7 × 15 × 42.7

→ 22 × 15 × 6.1

→ 330 × 6.1

→ 2013cm²

Hence, the surface area of the cone is 2013cm².