Multiple choice

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. The surface area of the solid is

  1. 16 cm2

  2. 418 cm2

  3. 485 cm2

  4. 16.6 cm2

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

The solid consists of a cylinder (height 19 - 7 = 12cm, radius 3.5cm) and two hemispheres (radius 3.5cm). Surface area = 2 * pi * r * h (cylinder) + 4 * pi * r^2 (sphere) = 2 * pi * 3.5 * 12 + 4 * pi * 3.5^2 = 84pi + 49pi = 133pi = 417.8 approx 418.

AI explanation

The total height is 19 cm and the diameter is 7 cm, so the radius r is 3.5 cm and the height of the cylindrical part is 19 minus the radii of the two hemispheres, giving 19 minus 7 which equals 12 cm. The surface area formula for this solid combines the curved surface of the cylinder and the two hemispheres, written as 2 * pi * r * h + 4 * pi * r^2, which is equivalent to 2 * (22 / 7) * 3.5 * 12 + 4 * (22 / 7) * 3.5^2. Calculating this gives 264 + 154, resulting in a total surface area of 418 square cm.

Keep practicing — related questions