Mensuration Questions

Multiple choice
  1. $\displaystyle 3000{ cm }^{ 3 }$
  2. $\displaystyle 1875{ cm }^{ 3 }$
  3. $\displaystyle 21875{ cm }^{ 3 }$
  4. $\displaystyle 1250{ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cardboard 25x35. Squares of area 25 (side 5) cut from corners. New dimensions: (25-10) = 15, (35-10) = 25. Height = 5. Volume = 15 * 25 * 5 = 1875.

Multiple choice
  1. $6\ hrs\ 40\ min$
  2. $6\ hrs$
  3. $5\ hrs$
  4. $7\ hrs$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The tank volume to be filled is 100 x 80 x 2 = 16,000 m^3. The flow rate is 1 x 40 = 40 m^3 per minute, so the time is 400 minutes, or 6 hours 40 minutes.

Multiple choice
  1. $\dfrac{4}{3}\pi r^{3}$
  2. $4\pi r^{3}$
  3. $\dfrac{8\pi r^{3}}{3}$
  4. $\dfrac{32}{3}\pi r^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a sphere is (4/3)pi*R^3. Given radius R = 2r, the volume is (4/3)*pi(2r)^3 = (4/3)*pi*8r^3 = (32/3)*pi*r^3.

Multiple choice
  1. $540 \displaystyle cm^{2}$
  2. $1080 \displaystyle cm^{2}$
  3. $2160 \displaystyle cm^{2}$
  4. $4320 \displaystyle cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circumference = 2 * pi * r = pi * d = 22/7 * 42 = 132. Perimeter of rectangle = 2(l+w) = 132, so l+w = 66. Ratio 6:5 means 6x + 5x = 66, so 11x = 66, x = 6. Sides are 36 and 30. Area = 36 * 30 = 1080.

Multiple choice
  1. $10 m$
  2. $9 m$
  3. $8 m$
  4. $7 m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let carpet side be x. Room dimensions are (x+2) and (x+4). Area of room = (x+2)(x+4) = x^2 + 6x + 8. Area of carpet = x^2. Uncarpeted area = (x^2 + 6x + 8) - x^2 = 6x + 8. 6x + 8 = 62, 6x = 54, x = 9.