Question

16) Find the radius of a cone whose slant height is 10 cm and height is 6 cm. 1 point
O 16 cm
O 4 cm
O 8 cm
O 136 cm​

Answer 1

• Option (c) 8 cm is correct.

Given :–

• Slant height of a cone (l) = 10 cm.
• Height of a cone (h) = 6 cm.

To Find :–

• Radius of a cone (r).

Solution :–

We know that,

$l = \sqrt{ {r}^{2} - {h}^{2} }$

Here, we need to find the value of r.

So,

$r = \sqrt{ {l}^{2} - {h}^{2} }$

Given that,

• Slant height (l) = 10 cm.
• Height (h) = 6 cm.

$r = \sqrt{ {(10 \: cm)}^{2} - {(6 \: cm)}^{2} }$

We know that,

• 10² = 100
• 6² = 36

$r = \sqrt{100 \: {cm}^{2} - {36 \: cm}^{2} }$

$r = \sqrt{64 \: {cm}^{2} }$

We know that,

• √64 = 8.

$r = 8 \: cm$

Hence,

The radius of a cone (r) is 8 cm.

So, the option (c) 8 cm is correct.

Additional Information :–

Some formulas of a cone :-

1. $\sf l = \sqrt{ {r}^{2} - {h}^{2} }$

2. $\sf r = \sqrt{ {l}^{2} - {h}^{2} }$

3. $\sf h = \sqrt{ {l}^{2} - {r}^{2} }$

4. Volume = $\sf \dfrac{1}{3}$πr²h

5. C.S.A. = πrh

6. T.S.A. = πr(h + r)