Question

In a cone of height 12 cm has a valume
616cm² the its diameter i
cm​

Answer 1

Correct Question :

In a cone of height 12 cm has a Volume

616cm³ . Then its diameter is ?

Given :

⬤ Height of Cone is 12 cm .

⬤ Volume of Cone is 616 cm² .

To Find :

⬤ Diameter of its Base .

Formula Used :

$\bf[\:{Volume\:of\:Cone=\dfrac{1}{3}\pi{r}^{2}h}\:]$

• r = radius
• h = height

Solution :

First , We have to Calculate Radius of the Cone . Hence ,

• Height = 12 cm .
• Volume of Cone = 616 cm³ .

According to the Formula :-

616 = 1/3πr²h

616 = 1/3 × 22/7 × r² × 12

(616×7) = 22 × r² × 4

4312 = 88 × r²

4312 = 88r²

4312/88 = r²

49 = r²

√49 = r

7 = r

Therefore , The Radius of Cone is 7 cm.

Now :

As we know that , Radius is Double of Diamater . Hence ,

R × 2

7 × 2

14

Therefore , The Diameter of the Cone is 14 cm.

Answer 2

$\underline{\purple{\mathfrak{Given \: -}}}$

• $\sf Height \: of \: the \: cone \: = \: 12cm$
• $\sf Volume \: of \: the \: cone \: = \: 616cm²$

$\underline{\purple{\mathfrak{To \: Find \: -}}}$

• $\sf Diameter \: of \: the \: base \: of \: the \: cone.$

$\underline{\purple{\mathfrak{as \: we \: know \: that \: -}}}$

$\boxed{\boxed{\bold\gray{Volume \: of \: a \: cone \: = \: \frac{1}{3}\pi \: r ²h}}}$

__________________

$\underline{\bold{\: \: \: \: \: \: \: \: \: According \: to \: question \: \: \: \: - \: \: \: \: }} \\ \\ :\sf\implies \: \frac{1}{3}\pi \: {r}^{2}h \: = 616 \\ \\ :\sf\implies \: \frac{1}{3} \times \frac{22}{7} \times r^{2} \times 12 = 616 \\ \\ :\sf\implies \: \frac{22}{7} \times \cancel \dfrac{12}{3} \: \times {r}^{2} = 616 \\ \\ :\sf\implies \: \frac{22}{7} \times 4 \times {r}^{2} = 616 \\ \\ :\sf\implies \: \frac{88}{7} \times {r}^{2} = 616 \\ \\ :\sf\implies \: {r}^{2} = \frac{616 \times 7}{88} \\ \\ :\sf\implies \: r ^{2} = \frac{4312}{88} \\ \\ :\sf\implies \: r^{2} = 49 \\ \\ :\sf\implies \: r \: = \sqrt{49} \\ \\ :\sf\implies \: r \: = \boxed{\bold\pink{7cm}} \: \bigstar$

_________________

$\sf\dashrightarrow$ Diameter = 2 × radius

$\sf\dashrightarrow$ Diameter = 2 × 7

$\sf\dashrightarrow$ Diameter = 14cm

_________________

$\sf\therefore \: Hence, \: the \: diameter \: of \: the \: base \: of \: the \: cone \: is \: \bold{14cm}\: .$