Question

The height of a cone is 15 cm.If its volume is 500π cm3, then find its diameter.

Answer 1

Given : The height of a cone is 15 cm and its volume is 500π cm³.

To  find : radius of its base.

Solution :  

We have , height,  h = 15 cm and volume,  V = 500π cm³

Let ‘r’ be the radius of its base.

Volume of the cone ,V = 1/3 πr²h

500 π = (1/3 × π × r² × 15)

500 =  5r²

r² = 500/5

r² = 100

r = √100

r = 10 cm

Radius = 10 cm  

Hence, the radius of its base is 10 cm.

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Answer 2

Answer:

• Diameter of cone is 20 cm.

Step-by-step explanation:

Given :-

• Height of cone is 15 cm.
• Volume of cone is 500π cm³.

To find :-

• Diameter of cone.

Solution :-

We know,

Volume of cone = 1/3 πr²h

Put volume and height in formula :

$\longrightarrow \sf 500 \: \pi = \dfrac{1}{\cancel{3}} \times \pi \times r^{2} \times \cancel{15}$

$\longrightarrow \sf 500 \: \pi = \pi \times r^{2} \times 5$

$\longrightarrow \sf \dfrac{500 \: \pi}{5} = \pi \: r^{2}$

$\longrightarrow \sf 100 \: \cancel{\pi} = \cancel{\pi} \times r^{2}$

$\longrightarrow \sf 100 = r^{2}$

$\longrightarrow \sf \sqrt{100} = r$

$\longrightarrow \sf r = 10$

Thus,

$\sf \bold{ \: Radius \: of \: cone \: is \: 10 \: cm.}$

Now,

Diameter = Radius × 2

$\longrightarrow \sf Diameter = 10 \times 2$

$\longrightarrow \sf Diameter = 20$

$\sf \bold{\therefore Diameter \: of \: cone \: is \: 20 \: cm.}$