Multiple choice

A right angle is enclosed by the sides of a triangle measuring 3.5 cm and 45 cm. The triangle is rotated about one of its longer perpendicular sides. Find the volume of the solid, thus traced.

  1. 144.3 cm3

  2. 454.3 cm3

  3. 577.5 cm3

  4. 664.6 cm3

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rotating the right-angled triangle about its longer perpendicular side (45 cm) forms a cone with a height of 45 cm and a base radius of 3.5 cm. The volume of this cone is (1/3) * pi * r^2 * h = (1/3) * (22/7) * 3.5 * 3.5 * 45, which simplifies to 577.5 cubic centimeters.

AI explanation

Rotating a right triangle about a perpendicular side forms a right circular cone with a height of 45 cm and a base radius of 3.5 cm. Using the volume of a cone formula, V = 1/3 * pi * r^2 * h, we substitute the values to get 1/3 * 22/7 * 3.5 * 3.5 * 45. This simplifies to 1/3 * 22 * 0.5 * 3.5 * 45, which equals 577.5 cm3.

Keep practicing — related questions