Question

4 How many coins each of thickness 0.1 cm and diameter 1.6cm will be melted to forma solid right circular cone of height 16 cm and diameter 4 cm?​

Answer 1

Given:

Thickness of the coin = 0.1 cm

Diameter of the coin = 1.6 cm

Height of right circular cone = 16 cm

Diameter of cone = 4 cm

To find:

No. of coins to be melted to form a right circular cone.

Solution:

Let $x$ be the no. of coins to be melted. The melted coins are used to form a right circular cone. That means, the volume of this cone will be equal to the volume of $x$ no. of coins.

Coin is in the shape of a very small cylinder having a thickness $t$ and diameter $d$.

Let the right circular cone formed by melting the coins have a height of $H$ and diameter $D$.

Volume of cone = $x$ × Volume of coin

$\frac{1}{3}\pi R^{2}H=x*\pi r^{2}t$

where $R$ is the radius of cone formed and $r$ is the radius of coin.

$R=\frac{D}{2}=\frac{4}{2}=2cm$

$r=\frac{d}{2}=\frac{1.6}{2} =0.8cm$

Substituting these values in the above equation to find no. of coins to be melted,

$\frac{1}{3}*2^{2}*16 =x*0.8^{2}*0.1$

$\frac{64}{3}=x*0.064$

$x=\frac{64}{3*0.064}$

$x=\frac{1000}{3}=333.34$

Since a number should be a whole number and not in fraction, we approximate to $333.$

So, the no. of coins to be melted to form a solid right circular cone is 333.

333 coins each of thickness 0.1cm and diameter 1.6cm are needed to melt into a solid right circular cone of height 16cm and diameter 4cm.

Answer 2

Answer:

The number of coins are $333$

Step-by-step explanation:

Given:

Thickness $0.1cm$

Diameter $1.6cm$

The volume of a coin will be

$=\pi r^2h\\\\=\pi (0.8)^2*0.1\\\\=0.064\pi$

The cone height $16cm$

the cone diameter $4cm$

The volume will be

$=\frac{1}{3} \pi r^2h\\\\=\frac{1}{3} \pi (2)^2*16\\\\=\frac{64\pi }{3}$

Equating to find  the number of coins then the condition is

$n*0.064\pi =\frac{64\pi }{3} \\\\n=\frac{1000}{3}\\\\n=333.33$