Question

the total surface area of cone with slant height 20cm and diameter of its base is 14M ​

Answer 1

Given -

• Slant height of cone = 20cm

• Diameter of base = 14m

To find -

• Total surface area of cone.

Formula used -

• T.S.A of cone

Solution -

In the question, we are provided with the slant height and base diameter, of a cone. Therefore, we will use the formula of total surface area of a cone, but before that we will convert base diameter into radius, by dividing Diameter by 2, as radius is half of diameter.

So -

Radius = $\sf\dfrac{Diameter}{2}$

Radius = $\sf\cancel\dfrac{14}{2}$

Radius = 7cm

Also -

The slant height is cm and base radius is in m, so we will convert cm into m.

Slant Height = 20cm

Slant height = $\sf\dfrac{Slant\: Height}{100}$

slant height = $\sf\dfrac{20}{100}$

Slant height = 0.2m

Now -

We will apply, the formula of TSA of cone, and then we will find the area of cone.

Total surface area of cone = πrl + πr²

where -

π = $\sf\dfrac{22}{7}$

r = Radius

l = slant Height

On substituting the values -

TSA = πrl + πr²

TSA = $\sf\dfrac{22}{7}$ × 7m × 0.2m + $\sf\dfrac{22}{7}$ × 49m

TSA = 22 × 0.2m² + 22 × 7m²

TSA = 4.4m² + 154m²

$\longrightarrow$ TSA = 158.4m²

$\therefore$ The TSA of cone is 158.4 m².

_____________________________________________________

Answer 2

Answer:

Given :-

• Slant height of cone = 20cm
• Diameter of base = 14m

To Find :-

TSA

Solution :-

Firstly let's convert the diameter into radius

$\tt \: Radius = \dfrac{ Diameter}{ 2}$

$\tt \: Radius = \cancel \frac{14}{2}$

$\mathfrak \orange{Radius = 7 \: m}$

Now,

Let's find TSA

As we know that

$\bf \: TSA = \pi rl + \pi r {}^{2}$

Here,

π is the 22/7

R is the Radius

L is the Slanght height

$\tt \: TSA = \dfrac{22}{7} (7)(20) + \dfrac{22}{7} (7) {}^{2}$

$\tt \: TSA = 22 \times 20 + \dfrac{22}{7} \times 49$

$\tt \: TSA = 22 \times 20 + 22 \times 7$

$\tt \: TSA \: = 450 + 154$

$\mathfrak \pink{TSA = 604 \: m {}^{3}}$

TSA of cone is 594m³.