Question

Q3 Solve the following:
1) The CS.A. surface area of a right circular cone is 528 cm. If the slant height of
the cone is 42 cm, find a) radius of the base, b) total surface area of the cone​

Answer 1

Answer:

a) 4 cm

b) 578.28 cm²

Step-by-step explanation:

Slant height of the cone ( l) = 42 cm

Let the radius of the base of the cone be ' r ' cm

CSA of the cone = 528 cm

We know that

CSA of a cone = πrl sq.units

=> 528 = 22/7 × r × 42

=> 528 = 22 × 6 × r

=> 528 / 22 × 6 = r

=> 4 = r

=> r = 4

Therefore the radius of the base is 4 cm.

We know that

TSA of a cone = πr × ( r + l ) sq.units

= 22/7 × 4 × ( 4 + 42 )

= 22/7 × 4 × 46

= 22/7 × 184

= 578.28 cm²

Therefore TSA of the cone is 578.28 cm².

Answer 2

Given Question :

The CS.A. surface area of a right circular cone is 528 cm. If the slant height of

the cone is 42 cm.

To Find :

◾Radius of the base

◾Total surface of cone

Formula Used :

$Curved \: surface \: area \: of \: Cone = \pi rl$

$Total \: surface \: area \: of \: cone = \pi rl + \pi {r}^{2}$

Solution :

According to the question,

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

And,

$Total \: surface \: area \: of \: cone = \pi rl + \pi {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 528 + \frac{22}{7} \times{4}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 528 + 50.28 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 578.28 \: {cm}^{2}$