Multiple choice

A pillar is made using a cylinder surmounted by a cone which is to be painted. The total height of the pillar is 10.25 feet and that of the cylinder is 6.25 feet. If the base area of the cylinder is 4π square feet, then what will be the area to be painted?

  1. 23.94π square feet

  2. 33.94π square feet

  3. 37.94π square feet

  4. 39.94π square feet
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The radius of the base is found using the base area formula, pi times r squared = 4 times pi, making r equal to 2 feet. The height of the cone is the total height minus the cylinder height, which is 10.25 minus 6.25 equals 4 feet. The slant height of the cone is found using the Pythagorean theorem, l = square root of (2 squared + 4 squared) equals square root of 20, which is approximately 4.47 feet. The total painted area is the curved surface area of the cone plus the curved surface area of the cylinder, calculated as (pi times 2 times 4.47) plus (pi times 2 times 2 times 6.25), resulting in approximately 33.94 times pi square feet.

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