Question

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. (Use π = 22/7).

Answer 1

We know that we can cut two circular pieces of equal radii and maximum area from the rectangular cardboard whose diameter is equal to the width of the rectangular cardboard.
∴ Radii of two circuar pieces = Half of the width of the rectangular cardboard = 3.5 cm
Now,
Area of remaining cardboard = Area of rectangular cardboard − 2 ⨯ Area of circular piece having radius 3.5 cm
$$\begin{gathered} =14\times 7-2\left(\frac{22}{7}\times 3.5\times 3.5\right) \\ =98-77 \\ =21{\mathrm{cm}}^2 \end{gathered}$$
=14×7−2(227×3.5×3.5)=98−77=21 cm2
Hence, the area of the remaining cardboard is 21 cm²