Question

) The C.S.A. surface area of a right circular cone is 528 cm'. If the slanthes
the cone is 42 cm, find a) radius of the base, b) total sus face area of the cone​

Answer 1

Answer:

• The curved surface area of right circular cone = 528 cm².
• The slant height of the cone = 42 cm.

The Formula to find the curved surface area of right circular cone = πrl.

Hence, 22/7 * r * 42 = 528

➸ r = 528 * 7/22 * 42

➸ r = 3,696/924

➸ Radius = 4 cm

➸ Radius = 4 cmHence, base radius = 4 cm.

The Formula to find the total surface area of a cone = πr(l + r).

Hence, 22/7 * 4 (42 + 4)

➸ 22/7 * 4 * 46

➸ 22/7 * 184

➸ 22 * 26.28

➸ 578.16 cm²

Hence, the total surface area of the cone = 578.16 cm².

CERTAIN IMPORTANT FORMULAS —

• TSA = πr(l + r)
• CSA = πrl
• Volume = ⅓ πr²h

Answer 2

Correct Question :

The C.S.A of right circular cone is 528 cm² .If the slant height of the cone is 42 cm. Find the radius of the base and T.S.A of the cone.

Given :

• The C.S.A of right circular cone is 528 cm² .
• The slant height of the cone is 42 cm.

To find :

• Radius of the base and T.S.A of the cone.

Solution :

Let the radius of the cone be r cm.

We know,

${\boxed{\bold{C.S.A\: of\: cone=\pi\:r\:l}}}$

Where,

• r = Radius
• l = Slant height

According to the question,

$\pi \: r \: l= 528 \\ \\ \implies \frac{22}{7 } \times r \times 42 = 528 \\ \\ \implies \: 22 \times 6 \times r = 528 \\ \\ \implies \: r = \frac{528}{22 \times 6} \\ \\ \implies \: r = 4$

Radius of the cone = 4 cm.

_______________________

We know,

${\boxed{\bold{T.S.A\:of\: cone=\pi\:r(r+l)}}}$

$\implies\sf{T.S.A=\pi\:r(r+l)}$

$\implies\sf{T.S.A=\frac{22}{7}\times\:4(4+42)\:cm^2}$

$\implies\sf{T.S.A=578.28\:cm^2\:(approx)}$

T.S.A of cone = 578.28 cm² (approx).

Therefore, the radius of the base is 4 cm and the T.S.A of the cone is 578.28 cm² ( approx ).