Multiple choice

The base of a prism is square and its height is 10 cm. If the whole surface area is 192 sq. cm, the volume of the prism is

  1. 160 cc.

  2. 165 cc.

  3. 170 cc.

  4. 150 cc.
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A Correct answer
Explanation

Let the side of the square base be 'a'. The surface area is 2a^2 + 4ah = 192. Given h=10, 2a^2 + 40a - 192 = 0, or a^2 + 20a - 96 = 0. Factoring gives (a+24)(a-4) = 0, so a = 4. The volume is a^2 * h = 4^2 * 10 = 160 cc.

AI explanation

The total surface area of a square prism is 2*(side)^2 added to 4*(side)(height), which gives the equation 192 equals 2(side)^2 plus 40*(side). Factoring the quadratic equation 2*(side)^2 + 40*(side) - 192 = 0 yields 2*(side + 24)*(side - 4) = 0, meaning the side is 4 cm. Applying the prism volume formula, Volume equals (4)^2 * 10, which is 160 cc.

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