Question

1. The diameter of the base of a cone of height 15cm and volume 770 cm
d) 10.5cm
a) 7cm
c) 21cm
b) 14cm
its​

Answer 1

bro ur answer is b) 14cm

Answer 2

Given:

A cone of height 15cm and volume 770 cm³

To find:

The diameter of the base of a cone

Solution:

The height of the cone, h = 15 cm

The volume of the cone, V = 770 cm³

Let "r" represent the radius of the base of the cone.

We know,

$\boxed{\boxed{\bold{Volume \:of\:a\:cone= \frac{1}{3} \pi r^2h}}}$

Now, substituting the given values in the formula of a cone above, we get

$770 = \frac{1}{3} \times \frac{22}{7} \times r^2\times 15}}}$

$\implies 770 = \frac{22}{7} \times r^2\times 5$

$\implies r^2 = \frac{770\:\times \:7}{22\:\times\: 5}$

$\implies r^2 = \frac{7\:\times \:11\times 10\times 7}{2\times 11\:\times\: 5}$

$\implies r^2 = 7\:\times \: 7$

$\implies \bold{r =7\:cm}$ ← base radius of the cone

∴ Base diameter = 2 × r = 2 × 7 = 14 cm

Thus, the final answer is → option (b) → The diameter of the base of the cone is 14 cm.

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