Question

areas of circular bases of frustum of a cone 4cm square and 16cm square. if 15 m height of the frustum then find volume of frustum

Answer 1

Answer:

Volume of frustum = 78.9 cm³

Step-by-step explanation:

Given : Areas of circular bases of frustum of a cone 4cm square and 16cm square. if 15 m height of the frustum.

To find: The volume of frustum?

Solution :

The ares of the circular bases of a frustum of a cone are 4 cm² and 9 cm²

So, let the radius of the upper base be 'R' and radius of the lower base be 'r'.

Now, Area of upper circular base = π·R²

⇒ 9 = π·R²

⇒ R = 1.69 cm

Area of lower circular base = π·r²

⇒ 4 = π·r²

⇒ r = 1.13 cm

r = 1.13 cm and R = 1.69 cm and height (h) = 12 cm

Now, we know that slant height of frustum, $l =\sqrt{h^2+(R - r)^2}$  where h is the height of the frustum.

$l =\sqrt{h^2+(1.69 - 1.13)^2}$

$l=\sqrt{12^2+(1.69 - 1.13)^2}$

$l=\sqrt{144+(0.56)^2}$

$l=\sqrt{144+0.03136}$

$l=\sqrt{144.03136}$

$l=12.001$

Volume of the frustum,

$V=\frac{1}{3}\pi h[r^2+R^2+Rr]$

$V=\frac{1}{3}(3.14)(12)[1.13^2+1.69^2+(1.13)(1.69)]$

$V=78.9$

Hence, Volume of frustum = 78.9 cm³.