Question

find the volume of a cone , if it's total surface area is 7128 Sq. cm and radius of base is 28 cm .(pie =22/7
plz answer it's urgent. .....

Answer 1

T.S.A.Cone= 7128
πr(l+r)=7128
22/7×28(l+28)=7128
88(l+28)=7128
88l + 2464=7128
88l=7128-2464
l=4604/88
l= 53
Now, to fine high 'h'=√l2-r2
√(53)2-(28)2
√2809-784
√2025
h=45
Volume of cone= 1/3πr2h
1/3×22/7×(28)2×45
1/3×22×112×45
22×112×15
36960.... Ans

Answer 2

Answer:  Volume of cone is 36960 cm³.

Step-by-step explanation:

Since we have given that

Total surface area of cone = 7128 cm²

Radius of cone = 28 cm

As we know the formula for "Total surface area of cone":

$\pi r(l+r)=7128\\\\\frac{22}{7}\times 28(l+28)=7128\\\\l+28=\frac{7128\times 7}{22\times 28}\\\\l+28=81\\\\l=81-28=53\ cm$

Now, we know the slant height 'l':

We will find the height of the cone":

$h=\sqrt{l^2-r^2}\\\\h=\sqrt{53^2-28^2}\\\\h=\sqrt{2025}\\\\h=45\ cm$

As we know the formula for "Volume of cone":

$Volume=\frac{1}{3}\pi r^2h\\\\Volume=\frac{1}{3}\times \frac{22}{7}\times 28\times 28\times 45\\\\Volume=36960\ cm^3$

Hence, Volume of cone is 36960 cm³.