Question

What is the capacity of a cone whose base area is 154cm square and height is 12 cm

Answer 1

What is the capacity of a cone whose base area is 154cm square and height is 12 cm ?

=> 1995.8 cm^3

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$\tt \underline{Given :}$

Base area = 154 sq.cm
Height = 12 metre

$\tt \underline{Solution :}$

As the base area = 154 sq.cm,

Area of circle = 154 cm^2

$\sf{πr^2 = 154 cm^2}$

$\sf{ \frac{22}{7} \times r {}^{2} = 154}$

$\sf{22r {}^{2} = 504 \times 7}$


$\sf{r {}^{2} = \frac{504 \times 7}{22}}$

$\sf{r {}^{2} = 22.9 \times 7}$

$\sf{r {}^{2} = 160.3}$

$\sf{r = 12.6}$


Now , Let's find the area of cone,

$\sf{Area \: of \: cone = \frac{1}{3} \times \pi \: r {}^{2}h}$

$\sf{ = \frac{1}{3} \times \frac{22}{7} \times 12.6 \times 12.6 \times 12}$

$\sf{= \frac{22}{7} \times 4.2 \times 12.6 \times 12}$

$\sf{= 22 \times 0.6 \times 12.6 \times 12}$

$\sf{= 166.3 \times 12}$

$\sf{= 1995.8 \: cm {}^{3} \: (approx)}$

Hence,

The capacity of a cone whose base area is 154cm square and height is 12 cm is 1995.8 cm^3 approximately.

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Answer 2

Hey ___!!

Question :-
What is Capacity Of Cone Whose Base Area Is 154 cm Square and Height is 12cm

Solution :-

Given :-

Base Area = 154cm square
Height = 12cm

To Find :- Volume Or Capacity Of Cone

Calculation :-

Base Area = 504 square (Given)

Formula Of Base of Area of Cone =

$\pi {r}^{2}$

Then,

$\pi {r}^{2} = {504cm}^{2}$

$\pi = \frac{22}{7}$

$\frac{22}{7} \times {r}^{2} = {504cm}^{2}$

${r}^{2} = \sqrt{160.36}$

$r = 12.66$

So ,

We Can Calculate Volume By Formula as We have Radius Now .

Volume Of Cone =

$\frac{1}{3} \pi {r}^{2} h$

Calculation :-

$\frac{1}{3} \times \frac{22}{7} \times 12.66 \times 12.66 \times 12$

$1 \times 22 \times 1.80 \times 12.66 \times 4$

$= 2005.344(approx)$

Thanks __!!