Question

Ramesh, an ice-cream seller, uses the container shown in the figure to freeze ice creams. He gets an order for 700 ice creams.
The density of ice cream 0.9167 g/cm³. [Use π = 22/7]
What quantity of ice cream should be freeze to complete the order?

a) 79.2 kg
b) 74.9 kg
c) 68.6 kg
d) 64.5 kg
​

Answer 1

$Given :-$

Ramesh, an ice-cream seller, uses the container shown in the figure to freeze ice creams. He gets an order for 700 ice creams.

The density of ice cream 0.9167 g/cm³. [Use π = 22/7]

What quantity of ice cream should be freeze to complete the order?

$Solution :-$

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

ius

\frac{7}{2}

rad

)

3.5 \: cm

=

Height (h) = 7cm

Volume of the cylinder = πr²h

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

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{2829.75}{21}

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

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 .

••••••

Answer 2

Given :

• Number of icecream ordered = 700
• Density of ice-cream = 0.9167 g/cm³

Ice-cream container is shown in figure, which is combination of

1) cylinder with,

• length = (10-3)cm = 7cm
• base radius= 2cm

2) Cone with

• length = (height) = 3cm
• base radius = 2cm

To find :

Quantity of ice-cream to complete order

Formula used :

• Volume of cylinder = πr²h
• Volume of cone = (1/3)πr²h
• Mass = Volume× Density

Solution :

First of all we need to find Volume of one container

Volume of one container = Volume of cylinder + volume of cone

$\sf \bullet \: Volume \: of \: cylinder \: = \: \: \dfrac{22}{ \not{7}} \times {(2 \: cm)}^{2} \times \not{7}cm \\ \\ \sf \implies \: Volume \: of \: cylinder \: = \: \:22 \times 4 \: {cm}^{3} \\ \\ \sf \implies \: Volume \: of \: cylinder \: = \: \:88 \: {cm}^{3} \\ \\ \\ \sf \bullet \: Volume \: of \: cone \: = \: \dfrac{1}{ \not{3}} \times \: \dfrac{22}{ {7}} \times {(2 \: cm)}^{2} \times \not{3}cm \\ \\ \sf \implies \: Volume \: of \: cone \: = \: \dfrac{22}{7} \times 4 \: {cm}^{3} \\ \\ \sf \implies \: Volume \: of \: cone \: = \: \dfrac{88}{7} \: {cm}^{3} \\ \\ \sf \implies \: Volume \: of \: cone \: = \: 12.57 \: {cm}^{3}$

➝ Total volume of one container = 88cm³ + 12.57cm³

➝ Total volume of one container = 100.57 cm³

_______________________________________________

Now quantity of ice-cream to be freezed for one container is given by

➝ Mass = Volume of one container × density

➝ Mass = 100.57 cm³ × (0.9167 cm³)

➝ Mass = 92.2 gram

_______________________________________________

Now , we have to find quantity for , 700 ice-creams,

➝ Mass = 700 × mass of one ice-cream

➝ Mass = 700 × 92.2 gram

➝ Mass = 64540 grams

➝ Mass = 64.54 kg ≈ 64.5 kg

ANSWER :

Option 4) 64.5 kg