Question

30. An ice-cream seller has two types of ice-cream container in the form of cylindrical shape and a
cone with hemispherical base. Both have same height of 7 cm and same diameter of 7 cm. The
costs of both the containers are same but the seller decides to sell in cylindrical containers.
(i) Calculate the volume of both containers.
(ii) Which value is depicted by the seller?

Answer 1

the value depicted here by seller is that as he know that volume of cylinder is more than the volume of cone with hemisphere as it comes consume more ice cream so he was knowledge full and smart

Answer 2

Answer:

i)Volume of the cylindrical container = 269.5cm³

ii)Volume of the cone with hemispherical base container

= 134.75 cm³

iii ) Volume of first container > Volume of second container

and

Price of both containers are same .

So, he get more profit he depicts first container price on second container.

Explanation:

i) Dimensions of a cylinder:

Diameter (d) = 7cm

radius (r)= $\frac{7}{2}$

= $3.5 \: cm$

Height (h) = 7cm

Volume of the cylinder = πr²h

= $\frac{22}{7}\times (3.5)^{2}\times 7$

= $269.5 \: cm^{3}$

Therefore,

Volume of the cylindrical container = 269.5cm³ -----(1)

ii ) Dimensions of the cone with hemispherical base container :

Radius of the base = cylinder base radius = 3.5 cm

Height of the container (H) =

7cm

Radius of the sphere (r)= 3.5cm

Height of the cone (h) = H-r

= 7 - 3.5

= 3.5 cm

Volume the container = volume of the cone + Volume of the sphere

= $\frac{1}{3}\times \pi\times r^{2} \times h+ \frac{2}{3} \times \pi\times r^{3}$

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

= $\frac{1}{3} \times \frac{22}{7} \times (3.5)^2 \times (3.5+2×3.5)$

= $\frac{1}{3} \times \frac{22}{7} \times 12.25 \times 10.5$

= $\frac{2829.75}{21}$

= $134.75 \: cm^{3}$

Therefore,

Volume of the cone with hemispherical base container

= 134.75 cm³ ----(2)

But ,cost of both containers are same

From , (1) and (2) we clearly

conclude that ,

(1) > (2)

seller decide to depict the price

on second containers which gives more profit than first container .

••••••