Multiple choice

A gift box in the shape of a right prism with a square base has a height of 20 centimetres. The total surface area of the gift box is 1,000 square centimetres. What will be the volume of the gift box in cubic centimetres?

  1. 1,500

  2. 1,600

  3. 1,800

  4. 2,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the side of the square base be s. The surface area is 2s^2 + 4sh = 1000. Given h = 20, we have 2s^2 + 80s - 1000 = 0, which simplifies to s^2 + 40s - 500 = 0. Solving for s gives (s+50)(s-10) = 0, so s = 10. The volume is s^2 * h = 10^2 * 20 = 2000.

AI explanation

Let the side of the square base be x centimetres, making the total surface area formula 2 times x squared plus 4 times x times 20 equal 1,000. This simplifies to x squared plus 40 x minus 500 equals 0, which solves to x equals 10. The volume formula for a prism is the base area times the height, giving 100 times 20, which equals 2,000 cubic centimetres.

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