Question

the total surface area of right circular cone is 628 4/7 CM^2 square if the radius of the base is 8 cm find the height of the cone​

Answer 1

SOLUTION:-

Given:

The total surface area of a right circular cone is 628 4/7. If the radius of its base is 8cm.

To find:

Find the height of the cone.

Solution:

According to the question:

We know that total surface area of a right circular cone;

=) πrl + πr²

Therefore,

$= > \frac{22}{7} \times 8 \times l + \frac{22}{7} \times8 \times 8 = \frac{4400}{7} \\ \\ = > \frac{176}{7} \times l + \frac{22}{7} \times 64 = \frac{4400}{7} \\ \\ = > \frac{176l}{7} + \frac{1408}{7} = \frac{4400}{7} \\ \\ = > \frac{176l}{7} = \frac{4400}{7} - \frac{1408}{7} \\ \\ = > \frac{176l}{7} = \frac{4400 - 1408}{7} \\ \\ = > \frac{176l}{7} = \frac{2992}{7} \\ \\ = > 176l = 2992 \\ \\ = > l = \frac{2992}{176} \\ \\ = > l = 17cm$

Now,

Height of the cone:

We know that,

=) l² = h² + r²

=) 17² = h² + 8²

=) 289= h² + 64

=) h² = 289 - 64

=) h² = 225

=) h= √225

=) h= 15cm

Thus,

Height of the cone is 15cm.

Hope it helps ☺️