Question

If area of a circle is 88.2 sq.m and π= 3.142, find r, correct to two significant figures.

Answer 1

Given, area of a circle = 88.2 sq.m, \(\pi\) = 3.142

But, area of a circle = \(\pi\)r²

\(\therefore\) 88.2 = 3.142 \(\times\) r²

Taking log on both sides, we get

log₁₀ 88.2 = log₁₀ 3.142 + log₁₀ r²

= log₁₀ 3.142 + 2 log₁₀ r

\(\therefore\) 2 log₁₀ r = log₁₀ 88.2 - log₁₀ 3.142

= 1.9455 - 0.4972 = 1.4483

\(\therefore\) log₁₀ r = 0.72415 = 0.7242

\(\therefore\) r = antilog (0.7242) = 5.299 = 5.30 m