Question

An ice-cream seller sells his to creams in two ways:
In a cone of radius $5cm$ and height $8cm$ with hemispherical top of same radius.
In a cylindrical cup of radius $5cm$ and height $8cm$.
He charges the same price for both, but prefers to sell his ice creams in the cone.
(a) Find the volume of the cone and the cup.
(b) Which out of two has more capacity?(c) By choosing a cone, which value is not followed by the ice cream seller?

Answer 1

(a). Volume of cone -

In cone $l=\sqrt{r^2+h^2}=\sqrt{5^2+8^2}$

$\Rightarrow$ Vol $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{2}\times \frac{22}{7}\times 25\times 8$

$=100\times 3.14c{m}^3$

$=314c{m}^3.$

$\Rightarrow$ Volume of cylinderical cup $=\pi r^{2}h$

$=3.14\times 25\times 8$

$=200\times 3.14c{m}^3$
$=628c{m}^3$

(b). cup have more capacity double that of cone.

(c). By choosing cone the ice cream seller is being dishonese.

Hence, solved.