Question

a right circular cone is 10m High and radius of its Base is 24 m . find its total Surface area .?​

Answer 1

Step-by-step explanation:

Given:-

• Height of the cone = 10m

• Radius of the cone = 24m

To Find:-

• Total surface area of the cone.

Solution:-

Height (h) = 10m , Radius (r) = 24cm

Let us find the slant height (l)

$\rm \dashrightarrow {l}^{2} = {r}^{2} + {h}^{2}$

$\rm \dashrightarrow {l}^{2} = {(24)}^{2} + {(10)}^{2}$

$\rm \dashrightarrow {l}^{2} = 576 + 100$

$\rm \dashrightarrow {l}^{2} = 676$

$\rm \dashrightarrow l= \sqrt{676} = 26$

$\rm \therefore Slant \: height \: (l)= 26m$

Total surface area of cone = πr(r + l)

$= \dfrac{22}{7} \times 24 \times (24 + 26)$

$= \dfrac{22}{7} \times 24 \times 50$

$= 3771.43$

$\underline{\boxed{\rm\therefore Total \: surface \: area \: of \: the \: cone = 3771.43cm^{2}}}$

Answer 2

Answer :-

★ Total Surface Area of Cone = 3771.43 m²

★ Concept -

Here the concept used is of Surface Area of Right Circular Cone. When, we are given with height and base radius, by finding out the slant height, we can get the surface area of cone.

This is formulated as :

• Surface area of cone = πr(r + L)

Where,

r = is the radius of base of cone

l = slant height of cone

★ Solution :-

Given,

• Radius of base of cone = r = 24 m

• Height of cone = h = 10 m

Then,

Slant height (L) is given by :-

✒ L² = h² + r²

By applying values, we get,

✒ L² = (10)² + (24)²

✒ L² = 100 + 576

✒ L² = 676

✒ L = √676 = 26

Hence, slant height of the cone = L = 26 m

Now using the formula of, Surface area of cone, we get,

✏ Surface Area = π × r(r + L)

✏ Surface Area = π × 24(24 + 26)

✏ Surface Area = π × 24 × 50

✏ Surface Area = π × 1200

✏ $surface \: area \: \: = \: (\dfrac{22}{7}) \times (1200)$

✏ Surface Area = 3771.43

Hence, Surface Area of the given cone =

3771.43 m²

★ More to know :-

• Surface Area of cone is the area of the curved surface of cone + area of the circular base of the cone.

It is denoted by (unit)².

• Curved Surface Area of cone is the area of only the curved surface of the cone.

It is denoted by (unit)² .

• Volume of the cone is the amount of gaseous space or better to say amount space occupied by gas into it.

It is denoted by (unit)³.

• The value of 'π' is taken as 22/7 as standard value if exact value isn't given.

• Note : mentioning the unit of the measurement is much important in terms of mensuration. So kindly mention it whenever you do according to the question. Here the unit is in 'm' so the answer will be in 'm²'.