Question

A toy is in the form of cone of radius r cm mounted on a hemisphere of the radius the total height of the toy is (r+ h) cm, find the volume of the toy​

Answer 1

☯ Given that,

• Radius of cone = Radius of hemisphere = r cm.
• Height of cone = h cm.
• The total height of the toy is (r + h) cm.

☯ To Find,

• The volume of the toy.

☯ Solution,

Let, volume of the toy be "x".

Volume of the toy = Volume of cone + Volume of hemisphere.

⇒ x = ¹/3 × πr²h + 2/3 × πr³

⇒ x = ¹/3 × 2/3 (πr²h + πr²)

⇒ x = 2/6 × πr²(h + 2r)

⇒ x = ¹/3 × πr²(h + 2r)

☯ Hence,

Volume of the toy is ¹/3 × πr²(h + 2r).

Answer 2

Answer:

The volume of the toy is $\frac{1}{3}\pi {r}^{2}(h + 2r)$

Step-by-step explanation:

Given that,

• A toy is in the form of cone.
• Radius of hemisphere = Radius of cone = r cm.
• Height of cone = (r + h) cm.

And,

• We need to find the volume of toy.

Now,

A toy is in the form of cone of radius r cm and and mounted on a hemisphere of the same radius.

Volume of toy = Volume of hemisphere + Volume of cone.

$= \frac{1}{3}\pi {r}^{2} h + \frac{2}{3}\pi {r}^{3} \\ \\ = \frac{\pi {r}^{2}h}{3} + \frac{2}{3}\pi {r}^{3} \\ \\ =\frac{\pi {r}^{2}h}{3} + \frac{2\pi {r}^{3} }{3} \\ \\ = \frac{\pi r {h}^{2} }{3} + \frac{2\pi {r}^{3} }{3} \\ \\ = \frac{\pi h {r}^{2} + 2\pi {r}^{3} }{3} \\ \\ = \frac{\pi{r}^{2}(h + 2r)}{3} \\ \\ = \frac{1}{3}\pi {r}^{2}(h + 2r)$

Hence, the volume of the toy is $\frac{1}{3}\pi {r}^{2}(h + 2r)$