Question

find the number of coins 2cm in diameter and 0.5cm to be melted to form a right circular cylinder of height 10cm and radius 3.5cm​

Answer 1

Answer:

The number of coins of diameter 2cm and height (thickness) 0.5cm required to melt and make a right circular cylinder of height 10cm and radius 3.5cm is 245.

Step-by-step explanation:

Radius of the right circular cylinder

R = 3.5cm

Height of the right circular cylinder

H = 10cm

Volume of the right circular cylinder

$V=\pi R^{2}H$

$V=3.14\times \left( 3.5\right) ^{2}\times 10$

$V=384.65cm^3$

Since coins are also right circular cylinders,

Diameter of the coins = 2cm

∴ Radius of the coins

r = 1cm

Height (thickness) of the coins

h = 0.5cm

Volume of one coin

$v=\pi r^{2}h$

$v=3.14\times \left( 1\right) ^{2}\times 0.5$

$v = 1.57cm^{3}$

Number of coins required to make the larger cylinder

$n = \frac{volume of the cylinder}{volume of one coin}$

$n = \frac{384.65}{1.57}$

$n = 245$

Therefore the number of coins required to make the larger cylinder is 245.