Question

Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm. (???? =22/7)

Answer 1

Hii..
Here is your answer..

Solution:-
Total surface area is given =7128 sq. cm
$= > \pi \: r(l + r) = 7128$
$= > \frac{22}{7} \times 28 \times (l + 28) = 7128$
$= > 88(l + 28) = 7128$
$= > 88l + 2464 = 7128$
$= > 88l = 7128 - 2464$
$= > 88l = 4604$
$= > l = \frac{4604}{88}$
$= > l = 53$
Now,
$height = \sqrt{ {l}^{2} - {r}^{2} }$
$= > \sqrt{ {53}^{2} - {28}^{2} }$
$= > \sqrt{2809 - 784}$
$= > \sqrt{2025}$
$= > 45$
$height = 45$
Since we know that,
Volume if cone =
$= > \frac{1}{3}\pi \: {r}^{2} h$
$= > \frac{1}{3} \times \frac{22}{7} \times {(28)}^{2} \times 45$
$= > \frac{1}{3} \times \frac{22}{7} \times 112 \times 45$
$= > 22 \times 112 \times 15$
$= > {36960 \: cm}^{3}$

Hope it helps uh...✌️✌️✌️