Question

A cone has a base of $5.4$ and a height of $8$. The diameter is $6$. What is the volume? If you were to dilate the cone with a scale factor of $2$, what would the new radius be?​

Answer 1

Solution :-

A cone has a base = 5.4 , height of the cone = 8 and

The diameter of the cone = 6

Radius = 6/2 = 3

Now,

We have to find the volume of the cone = ?

Therefore ,

The volume of the cone = 1/3hπr²

Subsitute the required values,

Volume of the cone

= 1/3 * 8 * 22/7 * 3 * 3

= 1/3 * 8 * 22/7 * 9

= 1/3 * 22/7 * 72

= 75.42

Thus, The volume of the cone is 75.42 .

Now, The cone is dilated by a scale factor of 2

So,

Radius of the cone after being dilated

= 3 * 2 = 6

Height of the cone after being dilated

= 8 * 2 = 16

Now,

Volume of the cone after being dilated

= 1/3 * 16 * 22/7 * 6 * 6

= 16 * 22/7 * 2 * 6

= 192 * 22/7

= 603.42

Hence, The new radius and the volume of the cone after being dilated is 6 and 603.42 $.$

Answer 2

$\huge\bf\fbox\red{Answer:-}$

A cone has a base = 5.4 , height of the cone = 8 and

The diameter of the cone = 6

Radius = 6/2 = 3

Now,

We have to find the volume of the cone=?

Therefore,

The volume of the cone = 1/3hπr²

Substitute the required values,

Volume of the cone

= 1/3 × 8 × 22/7 × 3 × 3

= 1/3 × 8 × 22/7 × 9

= 1/3 × 22/7 × 72

= 75.42

Thus, The volume of the cone is 75.42.

Now, The cone is dilated by a scale factor of 2

So,

Radius of the cone after being dilated

= 3 × 2 = 6

Height of the cone after being dilated

= 8 × 2 = 16

Now,

Volume of the cone after being dilated

= 1/3 × 16 × 22/7 × 6 × 6

= 16 × 22/7 × 2 × 6

= 192 × 22/7

= 603.42

Hence, The new radius and the volume of the cone after being dilated is 6 and 603.42.