Question

If the circumference of the colonial wooden price is 484 cm then find it's volume when its height is 105 cm

Answer 1

GIVEN:

• Circumference of conical piece = 484 cm
• Height of conical piece = 105 cm

TO FIND:

• What is the volume of the conical piece ?

SOLUTION:

Let the radius of the conical piece be 'r' cm

We know that the formula for finding the circumference is:-

 ❮ CIRCUMFERENCE = 2πr ❯

According to question:-

➠ 484 = 2 $\times$ $\sf{\dfrac{22}{7}}$$\times$ r

➠ 484 $\times$ 7 = 2 $\times$ 22 $\times$ r

➠ 3388 = 44 $\times$ r

➠ $\sf{\cancel\dfrac{3388}{44} = r}$

✫ 77 cm = r ✫

To find the volume of conical piece, we use the formula:-

 ❮ VOLUME = $\bf{\dfrac{1}{3}}$ πr²h ❯ 

According to question:-

On putting the given values in the formula, we get

➠ V = $\sf{\dfrac{1}{3}}$ $\times$ $\sf{\dfrac{22}{7}}$ $\times$ (77)² $\times$ 105 cm

➠ V = $\sf{\dfrac{22}{7}}$$\times$ 5929 $\times$ 35

➠ V = 22 $\times$ 847 $\times$ 35

✫ V = 652190 cm³ ✫

❝ Hence, the volume of conical piece is 652190 cm³ ❞

______________________

Answer 2

$\huge\underline\mathfrak{Given:}$

• The circumference of the wooden conical piece = 484 cm.

• The height of the conical piece = 105 cm.

$\huge\underline\mathfrak{To \: Find:}$

• The volume of the conical piece.

$\huge\underline\mathfrak{Solution:}$

We know the formula of circumference = 2πr

Now,

According to the question,

$\rm{\implies \: 484 = 2\pi r}$

$\rm{\implies 484 = 2 \times \frac{22}{7} \times r}$

$\rm{\implies 484 = \frac{44}{7} \times r}$

$\rm{\implies 44r = 484 \times 7}$

$\rm{\implies 44r = 3388}$

$\rm{\implies r =\cancel \frac{3388}{44} }$

$\rm{\implies r = 77 \: cm}$

$\rule{300}{2}$

Now ,we know the formula of volume

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

Again, by condition,

$\rm{</u><u>V</u><u>olume = \frac{1}{3} \times \frac{22}{7} \times</u><u> </u><u>77 \times 77\times 105}$

$\rm{\implies \: Volume = \frac{22}{21} \times 5929 \times 105}$

$\rm{\implies Volume = 22 \times 5929 \times 5}$

$\rm{\implies Volume = 130438 \times 5}$

$\rm{\implies Volume = 652190 \: {cm}^{3} }$

Hence,the volume of the conical piece is 652190 cm².