Arithmetic aptitude :: Area :: General Questions

• Area - General Questions

If the radius of a circle is increased by 75%, then its circumference will increase by :

Answer:

Explanation:

Let original radius be $R$ cm. Then, original circumference $=2\pi R$ cm.

New radius = ($175\%$ of $R$)cm $=\left(\frac{175}{100}\times R\right)$ cm $=\frac{7R}{4}$ cm.

New circumference $=\left(2\pi\times\frac{7R}{4}\right)$ cm $=\frac{7\pi R}{2}$ cm.

Increase in circumference $=\left(\frac{7\pi R}{2}-2\pi R\right)$ cm $=\frac{3\pi R}{2}$ cm.

Increase % $=\left(\frac{3\pi R}{2}\times\frac{1}{2\pi R}\times 100\right)$% = 75%.

An equilateral triangle, a square and a circle have equal perimeters. If $T$, denotes the area of the triangle, $S$, the area of the square and $C$, the area of the circle, then :

Answer:

Explanation:

Let the perimeter of each be $a$.

Then, side of the equilateral triangle $=\frac{a}{3}$: side of the square $=\frac{a}{4}$;

Radius of the circle $=\frac{a}{2\pi}$.

$\therefore T$ $=\frac{\sqrt{3}}{4}$ $\times\left(\frac{a}{3}\right)^{2}$

$=\frac{\sqrt{3}a^{2}}{36}$; $S=\left(\frac{a}{4}\right)^{2}$

$=\frac{a^{2}}{16}$; $C$ $=\pi\times\left(\frac{a}{2\pi}\right)^{2}$ $=\frac{a^{2}}{4\pi}$

$=\frac{7a^{2}}{88}$.

So, $C>S>T$.

There are 4 semi-circular gardens on each side of a square-shaped pond with each side 21m. The cost of fencing the entire plot at the rate of Rs 12.50 per metre is :

Answer:

Explanation:

What will be the area of a semi-circle of 14 m diameter ?

Answer:

Explanation:

The areas of two concentric circles forming a ring are 154 sq. cm and 616 sq. cm. The breadth of the ring is :

Answer:

Explanation:

• Area - General Questions