Question

If the volume of a right circular cone of height 12 cm is 100 cm3, find the diameter of its
base.
​

Answer 1

Given :-

• Height = 12 cm.

• Volume = 100cm³

To Find :-

• Diameter Of Base.

Solution :-

We know that,

$\boxed{\sf{Volume \: of \: cone \: = \dfrac{1}{3} \pi \: {r}^{2} h}}$

Put the given Values.

$\dashrightarrow\sf{100 = \dfrac{1}{3} \times \dfrac{22}{7} \times 12 \times {r}^{2}}$

$\dashrightarrow\sf{\dfrac{264}{21}{r}^{2} = 100}$

$\dashrightarrow\sf{264{r}^{2} = 100 \times 21 }$

$\dashrightarrow\sf{{r}^{2} = \dfrac{2100}{264}}$

$\dashrightarrow\sf{r = \sqrt\dfrac{2100}{264}}$

$\dashrightarrow\sf{r = \sqrt{7.95}}$

$\dashrightarrow\bf\red{ 2.82 cm \: (approx)}$

Now, Diameter Of Base = 2 × Radius.

2 × 2.82 = 5.64 cm. (Approx.)

Hence, This is your required answer.

Answer 2

Answer:

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