Find the number of metallic circular discs with 1.5 cm base diameter and height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
450 discs
Step 1: Write the formula for the volume of a cylinder.
The volume of a cylinder is given by:
\( V = \pi r^2 h \)
where \( r \) = radius of the base, and \( h \) = height of the cylinder.
Step 2: Find the volume of one small disc.
Given diameter of the disc = 1.5 cm, so radius \( r = \dfrac{1.5}{2} = 0.75\,cm \).
Height of disc \( h = 0.2\,cm \).
Now, volume of one disc:
\( V_{disc} = \pi (0.75)^2 (0.2) = \pi (0.5625)(0.2) = 0.1125\pi \; cm^3 \).
Step 3: Find the volume of the bigger cylinder.
Given diameter of big cylinder = 4.5 cm, so radius \( r = \dfrac{4.5}{2} = 2.25\,cm \).
Height of big cylinder \( h = 10\,cm \).
Now, volume of big cylinder:
\( V_{big} = \pi (2.25)^2 (10) = \pi (5.0625)(10) = 50.625\pi \; cm^3 \).
Step 4: Calculate how many discs are needed.
Since all the discs are melted and formed into the big cylinder, total number of discs =
\( \dfrac{\text{Volume of big cylinder}}{\text{Volume of one disc}} = \dfrac{50.625\pi}{0.1125\pi} \).
\( \pi \) cancels out.
So, \( \dfrac{50.625}{0.1125} = 450 \).
Final Answer: 450 discs are required.