Multiple choice

A triangular copper plate with sides of $3$ cm, $4$ cm and $5$ cm It has three small circular holes cut out of it The radius of each circle is $3$ mm. What is the area of the copper remaining

  1.  $6\displaystyle cm^{2}$
  2. $5.16\displaystyle cm^{2}$
  3. $5.9973\displaystyle cm^{2}$
  4. $5.71\displaystyle cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The 3 cm, 4 cm, 5 cm triangle is right-angled, so its area is (3 x 4)/2 = 6 cm^2. Each hole has radius 0.3 cm, and the total area removed is 3 x pi x 0.3^2, approximately 0.848 cm^2. The remaining area is approximately 6 - 0.848 = 5.16 cm^2.

AI explanation

The sides of 3 cm, 4 cm, and 5 cm form a right triangle, so the area of the copper plate is one half times 3 times 4, which equals 6 square cm. Each hole has a radius of 3 mm, which converts to 0.3 cm, making the area of one hole pi times 0.3 squared, or approximately 0.2827 square cm. For three holes, the total removed area is about 0.8482 square cm. Subtracting this from the plate area leaves 6 minus 0.8482, resulting in 5.1518 square cm, which rounds to 5.16 square cm.

Keep practicing — related questions