Question

c. The circumference of the base of a right circular cone is 22cm and its slant height is 8cm. Its

curved surface area is:

i. 100cm2

ii. 90cm2

iii. 88cm2

iv. 77cm2​

Answer 1

Question:

• The circumference of the base of a right circular cone is 22 cm and its slant height is 8 cm. It's curved surface area is:

• i. 100 cm²
• ii. 90 cm²
• iii. 88 cm²
• iv. 77 cm²

Answer:

• Curved surface area of right circular cone is iii. 88 cm².

Explanation:

Given:

• Circumference of the base of a right circular cone = 22 cm
• Slant height of right circular cone (l) = 8cm

To Find:

• It's curved surface area (CSA) ?

Solution:

• Firstly, let's find radius of base of cone (r) ::

We know that,

✪ $\boxed{\bf{Circumference\: of\: circle = 2\pi r}}$ ✪

According the question by using the formula we get,

➻ $\sf 2 \:\times\:\dfrac{22}{7} \:\times\: r = 22$

➻ $\sf r = \cancel{22} \:\times\:\dfrac{7}{\cancel{22}}\:\times\: \dfrac{1}{2}$

➻ $\sf r = \dfrac{7 \:\times\: 1}{2}$

➻ $\bf \red{r = \dfrac{7}{2}\:cm}$

∴ Hence, base radius of cone is 7/2 cm.

Now,

we know that,

✪ $\boxed{\bf{CSA \:of \:cone = \pi rl}}$ ✪

According the question by using the formula we get,

➻ $\sf CSA\:of\:cone = \dfrac{22}{\cancel{7}} \:\times\:\dfrac{\cancel{7}}{2} \:\times\:8$

➻ $\sf CSA\:of\:cone = {\cancel{\dfrac{22}{2}}} \:\times\:8$

➻ $\sf CSA\:of\:cone = 11 \:\times\: 8$

➻ $\bf\purple{CSA\:of\:cone = 88\:cm^2}$

∴ Hence, curved surface area of cone is 88 cm² (Option iii. 88 cm² is correct).

Know more:

✧ Some surface area formulae ✧

• TSA of cube = 6a²
• CSA of cube = 4a²
• TSA of cuboid = 2(lb + bh + hl)
• CSA of cuboid = 2(l + b)h
• TSA of cylinder = 2πr(r + h)
• CSA of cylinder = 2πrh
• TSA of cone = πr(l + r)
• CSA of cone = πrl
• SA of sphere = 4πr²
• TSA of hemisphere = 3πr²
• CSA of hemisphere = 2πr²

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Answer:

iii. 88cm²

The curved surface area (C.S.A.) of cone = 88cm²

Step-by-step explanation:

Given:

The circumference of the base of a right circular cone = 22 cm.

The slant height of the cone (l) = 8 cm

To Find:

The curved surface area (C.S.A.) of cone.

Solution:

Circumference of the base of cone = 22 cm.

We know that,

Circumference = 2πr

So,

=> 2πr = 22 cm

=> 2*22/7*r = 22 cm

=> 22/7*r = 22/2 cm

=> r = 22*7/2*22 cm

=> r = 7/2 cm

=> r = 3.5 cm

Therefore, the radius of the base (r) is 3.5 cm.

Now,

Slant height of the cone (l) = 8 cm.

We know that,

Curved surface area (C.S.A.) of the cone = πrl

=> 22/7*3.5cm*8 cm

=> 22/7*35/10*8 cm²

=> 22*5/10*8 cm²

=> 22*1/2*8 cm²

=> 11*8 cm²

=> 88 cm²

Hence,

The option (iii) is correct.

The curved surface area of cone is 88cm².