Question

An ice-cream seller sells his ice - creams in two ways

(A) In a cone of $r = 5cm,h = 8cm$ with a hemispherical top.

(B) In a cup in shape of cylinder with $r = 5cm,h = 8cm$

He charges the same price for both but prefers to sell his ice-cream in a cone.

(a) Find the volume of the cone and the cup.

(b) Which out of the two has more capacity?

(c) By choosing a cone, which value is not being followed by the ice-cream seller?

Answer 1

Hint- In order to deal with this question we will evaluate the volume of cup and cone by using the formula which is mentioned in the solution further we will see which one is greater at last ice cream seller will not follow the shape which has greater volume.

Complete step-by-step answer:

a) Given that cone of $r = 5cm,h = 8cm$with a hemispherical top
As we know that
Volume of cone = $\dfrac{1}{3}\pi {r^2}h$
And volume of hemisphere = $\dfrac{2}{3}\pi {r^3}$
So volume of type ‘A’ = Volume of cone + Volume of hemisphere
$ = \dfrac{1}{3}\pi {r^2}h$$ = \dfrac{1}{3}\pi {r^2}h + \dfrac{2}{3}\pi {r^3}$
Substitute the given values in above formula we have
$
   = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 5 \times 5 \times 8 + \dfrac{2}{3} \times \dfrac{{22}}{7} \times 5 \times 5 \times 5 \\
   = \dfrac{{22}}{7} \times 5 \times 5\left[ {\dfrac{8}{3} + \dfrac{{10}}{3}} \right] \\
   = \dfrac{{22}}{7} \times 25 \times 6 \\
   = \dfrac{{3300}}{7} \\
   = 471.43{(cm)^3} \\
$
Now , Volume of type ‘B’ = Volume of cylinder
As we know that
Volume of cylinder = $\pi {r^2}h$
So, Volume of type ‘B’ = $\pi {r^2}h$
Substitute the given values in above formula we get
$
   = \dfrac{{22}}{7} \times 5 \times 5 \times 8 \\
   = \dfrac{{4400}}{7} \\
   = 628.57{(cm)^3} \\
$
Volume of a cone = \[471.43{\text{ (}}cm{)^3}\]
Volume of a cup =\[{\text{628}}{\text{.57 (}}cm{)^3}\]

(b) By seeing the volumes of both cup and cone we can say that Cup has more capacity than Cone.

(c) By choosing a cone he is not following the value of honesty because cone volume is less than from volume of cup.

Note- Volume of a cone is give by $ = \dfrac{1}{3}\pi {r^2}h$ where $r$is the radius of the cone and $h$ is the height of the cone , volume of hemisphere is given by $\dfrac{2}{3}\pi {r^3}$ whereas the volume of the cylinder is given by $\pi {r^2}h$ where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.