Question

By melting a solid cuboid of length 16 cm, height 10cm and breadth 11cm
how many coins of 0.2cm
thickness and 2cm diametere can be formed
?
a)2200
b)2400
c)2600
d)2800
explain step by step​

Answer 1

ANSWER :-

• Option D) 2800.

GIVEN :-

• Solid Cuboid of length 16cm , breadth 11cm and height 10cm is melted to form coins of diameter 2cm and thickness 0.2cm.

TO FIND :-

• Number of coins formed.

TO KNOW :-

★ Volume of Cuboid = l × b × h

★ Volume of Cylinder = πr²h

SOLUTION :-

Coin is in the shape of Cylinder.

As Cuboid is melted to form coins ,

Volume of Cuboid = Volume of Total coins

Let the Total number of coins be 'n'.

Volume of Cuboid = n × Volume of one coin

l × b × h = n × πr²H

♦ For Cuboid ,

• Length (l) = 16cm
• Breadth (b) = 11cm
• Height (h) = 10cm

♦ For coin ,

• Radius = D/2 = 2/2 = 1cm
• H = 0.2cn

Putting values,

→ 16 × 11 × 10 = n × (22/7) × (1)² × 0.2

→ 1760 = n × (4.4/7)

→ n = (1760×7)/4.4

→ n = 12320/4.4

→ n = 2800

Hence , 2800 coins can be formed. Option D.

MORE TO KNOW :-

★ Volume of Cone = (1/3)πr²h

★ Volume of Cube = edge³

★ Volume of Sphere = (4/3)πr³

★ Volume of Hemisphere = (2/3)πr³

Answer 2

2800

Option D [ ✓ ]

Given :

• Melting a solid cuboid of length = 16 cm
• Height 10cm
• Breadth 11cm

To find :

• How many coins for 0.2cm ?

Formual used :

l × b × h

Solution :

16 × 11 × 10

= 1760 cm³

The thickness of coin = 2 mm = 0.2 cm

∵ 1 cm = 10 mm

The diameter of coin = 2 cm

Therefore ,

Radius of coin (R)

$= \frac{D}{2} = \frac{2}{2} = 1cm \:$

Hence , Volume of coin = πR²H

$= \frac{22}{7} \times 1 {}^{2} \times 0.2$

$= \frac{4.4}{7} cm³$

Number of coins that are made =

$= \frac{volume \: of \: \: parelopiped}{volume \: of \: one \: coin}$

$= \frac{1760}{( \frac{4.4}{7}) }$

$= \frac{1760 \times 7}{4.4}$

$= \frac{1760 \times 7 \times 10}{44}$

$= 2800$

Hence , Number of coins made are 2800 ✓