Question

9. If the volume of a right circular cone of height 12 cm is 100 cm find the diameter of its base.
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Answer 1

Answer:

Diameter of the base is 25 cm

Step-by-step explanation:

Volume = 1/3 π r² h

Volume = 1/3 π r² h

100π   =  1/3 π r² ×12

:. r²=25

:. r=5

Answer 2

Given -

• Height = 12 cm

• Volume = 100cm³

To Find -

• Diameter Of Base.

Solution -

We know that, the volume of cone is $\sf\dfrac{1}{3}$πr²h and here, we are provided with the volume and height of the cone, and we have to find the base diameter.

So -

Volume = $\sf\dfrac{1}{3}$ πr²h

On substituting the values -

Volume = $\sf\dfrac{1}{3}$ πr²h

$\longmapsto$ Volume = $\sf\dfrac{1}{3}$ × $\sf\dfrac{22}{7}$ × (r)² × 12cm

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

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

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

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

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

$\longmapsto$ r = $\sf{2.82 cm}$

Now -

As per the requirement of the question, we need to find the base diameter of the cone, so we will multiply the radius with 2, aa diameter is double of radius.

so -

Diameter Of Base = 2 × Radius.

2 × 2.82 = 5.64 cm.

$\therefore$ The base diameter of the cone is 5.64cm

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