Question

If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. If the cost of flooring the boundary by tiles is Rs 50 per square metre, then the cost incurred will be

• A. 352800
• B. 350000
• C. 375000
• D. 352500

Answer 1

The correct option is A 352800

We have, OB = O'C = 35 m
and AB = CD =14 m

Also, AD = FG =120 m
Now, OA = O'D = (35+14) = 49 m

Area of the region (boundary) = Area of rectangle ABCD + Area of rectangle EFGH +2 {area of semi-circle with centre O and radius 49 m -Area of semi-circle with radius 35 m}
$=120\times 14+120\times 14+2(\frac{1}{2}\times \frac{22}{7}\times {49}^2-\frac{1}{2}\times \frac{22}{7}\times {35}^2)=[1680+1680+\frac{22}{7}({49}^2-{35}^2\left)\right]=[3360+\frac{22}{7}(49+35\left)\right(49-35\left)\right]=3360+3696=7056m^2$

Cost of flooring per sq metre = Rs 50
Cost of flooring $7056m^2=7056\times 50=Rs352800$