Mensuration Questions

Multiple choice
  1. $1.54\ cm^2 $
  2. $0.77\ cm^2 $
  3. $6.16\ cm^2 $
  4. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The diameter is 1.4 cm, so the radius is 0.7 cm. The area is pi * r^2 = (22/7) * 0.7 * 0.7 = 22 * 0.07 = 1.54 cm^2.

Multiple choice
  1. $3850 \: cm^{2}$
  2. $2850 \: cm^{2}$
  3. $1850 \: cm^{2}$
  4. $4850 \: cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circumference 1 = 2*pi*48, Circumference 2 = 2*pi*13. Difference = 2*pi*(48-13) = 2*pi*35. New circle circumference = 2*pi*r = 2*pi*35, so r = 35. Area = pi * 35^2 = 1225 * 22/7 = 3850.

Multiple choice
  1. $616 \: cm^{2}$
  2. $516 \: cm^{2}$
  3. $116 \: cm^{2}$
  4. $216 \: cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The radius r is half the diameter, so r = 14 cm. The area of a circle is pi * r^2. Using 22/7 for pi, the area is (22/7) * 14 * 14 = 22 * 2 * 14 = 616 cm^2.

Multiple choice
  1. $1039.5 \: cm^{2}$
  2. $1339.5 \: cm^{2}$
  3. $1239.5 \: cm^{2}$
  4. $1139.5 \: cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let diameters be 3k, 5k, 6k. Circumferences are pi*3k + pi*5k + pi*6k = 14*pi*k = 308. So k = 308/(14*pi) = 22/pi. Radii are 1.5k, 2.5k, 3k. Difference in areas = pi*(3k)^2 - pi*(1.5k)^2 = pi*k^2*(9 - 2.25) = 6.75*pi*k^2. Substituting k = 22/pi gives 6.75*pi*(22/pi)^2 = 6.75 * 484 / (22/7) = 1039.5.