Mensuration Practice Test 1

Question : 35 of 40

Marks: +1, -0

A circular grass plot 4 m in diameter is cut by a straight path of 1 m wide, one edge of which passes through the centre of the plot. The area of the remaining portion is:

${4π}/3 - √3$
${10π}/3 -√2$
${10π}/3 + √3$
${7π}/2$

Validate

Solution:

In AOC by Pythagoras Theorem,
AC =

√{2^2-1^2}

√{4-1}

√3

AC =

√3

AB =

2√3

Area of semicircle =

π/2 × (√3)^2

{3π}/2

Area of semicircle =

π/2 × 2 × 2

2π

Sum of semicircle =

{3π}/2 + 2π

{3π+4π}/2

{7π}/2

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