Question 74

Thrice the length of the diameter of a circle is 10 cm less than its circumference. What is the radius of the circle? [Use $$\pi = \frac{22}{7}$$]

Solution

Let's assume the radius of the circle is 'r'.

Thrice the length of the diameter of a circle is 10 cm less than its circumference.

$$3\times diameter = circumference - 10$$

$$3\times2r=2\times\ \pi\ \times\ r-10$$

$$3\times2r=2\times\frac{22}{7}\times\ r-10$$

$$6r=\frac{44}{7}r-10$$

$$\frac{44}{7}r-6r=10$$

$$\frac{44r-42r}{7}=10$$
$$\frac{2r}{7}=10$$
$$\frac{r}{7}=5$$
radius of the circle = r = 35 cm

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