Multiple choice

The sides of a rectangle with dimension 7 cm x 11 cm are joined to form a cylinder with height 11 cm. What is the volume of this cylinder?

  1. 85.75 cm3

  2. 86.92 cm3

  3. 54.25 cm3

  4. 42.875 cm3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a rectangle of 7x11 is joined to form a cylinder with height 11, the circumference is 7. So 2 * pi * r = 7, which means r = 7 / (2 * pi). Volume = pi * r^2 * h = pi * (7 / (2 * pi))^2 * 11 = pi * (49 / (4 * pi^2)) * 11 = (49 * 11) / (4 * pi) = 539 / (4 * 3.14159) = 42.875.

AI explanation

When the rectangle with dimensions 7 cm by 11 cm is rolled to form a cylinder with a height of 11 cm, its 7 cm side becomes the circumference of the base. Using the circumference formula 2 times pi times r equals 7, the radius of the cylinder is 7 divided by 2 times pi. The volume formula for a cylinder is pi times r squared times height, which gives pi times (7 divided by 2 times pi) squared times 11. This simplifies to (49 divided by 4 times pi) times 11, which is approximately 42.875 cm3.

Keep practicing — related questions