Mensuration Questions

Multiple choice
  1. $\displaystyle 88{ ft }^{ 2 }$
  2. $\displaystyle 198{ ft }^{ 2 }$
  3. $\displaystyle 79{ ft }^{ 2 }$
  4. $\displaystyle 176{ ft }^{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume = pi * r^2 * h = 616. (22/7) * r^2 * 4 = 616. r^2 = 616 * 7 / 88 = 49. r = 7. Curved surface area = 2 * pi * r * h = 2 * (22/7) * 7 * 4 = 176 sq ft.

Multiple choice
  1. $\displaystyle 23936{\  ft }^{ 3 }$
  2. $\displaystyle 23936{\  ft }^{ 2 }$
  3. $\displaystyle 23950{ \ ft }^{ 2 }$
  4. $\displaystyle 23936\ ft$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The surface area of a cylinder is 2 * pi * r * h + 2 * pi * r^2. Given h = 12 and r = 56, the area is 2 * pi * 56 * 12 + 2 * pi * 56^2. This equals 1344 * pi + 6272 * pi = 7616 * pi. Using pi approx 3.14159, 7616 * 3.14159 is approx 23926. The option 23936 is the closest value.

Multiple choice
  1. $\displaystyle 140.5{ m }^{ 2 }$
  2. $\displaystyle 422.02{ m }^{ 2 }$
  3. $\displaystyle 150.2{ m }^{ 2 }$
  4. $\displaystyle 142.8{ m }^{ 3 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume V = pi * r^2 * h = 400. With r=7, 400 = pi * 49 * h, so h = 400 / (49 * pi) approx 2.598. Total surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 2.598) approx 422.02.

Multiple choice
  1. $\displaystyle 2 $ ${ mm }$
  2. $\displaystyle 3 $ ${ mm }$
  3. $\displaystyle 4 $ ${ mm }$
  4. $\displaystyle 5 $ ${ mm }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area of a cylinder = 2 * pi * r * (r + h). 132 = 2 * (22/7) * r * (r + 4). 132 * 7 / 44 = r(r+4) => 21 = r^2 + 4r => r^2 + 4r - 21 = 0. (r+7)(r-3) = 0. Since radius must be positive, r = 3.

Multiple choice
  1. $10$ in
  2. $9.65$ in
  3. $9$ in
  4. $9.5$ in
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The surface area of a cylinder is 2 * pi * r * (r + h) = 590. Given r = 6 and pi = 3.14, we have 2 * 3.14 * 6 * (6 + h) = 590. This simplifies to 37.68 * (6 + h) = 590, so 6 + h = 15.658, and h = 9.658.

Multiple choice
  1. $\displaystyle 110.126{ cm }^{ 2 }$
  2. $\displaystyle 110.916{ cm }^{ 2 }$
  3. $\displaystyle 348.27{ cm }^{ 3 }$
  4. $\displaystyle 345.425{ cm }^{ 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The height is 11 cm because it is twice the radius. The volume is 1/3 times pi times 5.5^2 times 11, approximately 348.27 cm^3, so option C has the correct numerical value, although its unit should be cm^3 rather than cm^2.