Question : What is the volume of a cube whose surface area is 54 cm2?
Option 1: 28 cm3
Option 2: 3 cm3
Option 3: 27 cm3
Option 4: 9 cm3
Correct Answer: 27 cm3
Solution : Given, Surface area of cube = 54 cm2 Let the length of the sides of the cube be a. We know that the surface area of a cube = 6a2 Volume of a cube = a3 According to the question, Surface Area = 6a2 ⇒ 54 = 6a2 ⇒ a2 = 9 ⇒ a = $\sqrt{9}$ = 3 cm Now, the volume of the cube = (3)3 = 27 cm3 Hence, the correct answer is 27 cm3.
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Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : What is the difference between the total surface area and the curved surface area of a cone whose radius is 35 cm? (Take $\pi=\frac{22}{7}$)
Option 1: 3850 cm2
Option 2: 3704 cm2
Option 3: 3750 cm2
Option 4: 3675 cm2
Question : The base of the right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm2, then its volume is:
Option 1: 3 cm3
Option 2: 1 cm3
Option 3: 2 cm3
Option 4: 4 cm3
Question : The base of a solid right prism is a triangle whose sides are 9 cm, 12 cm, and 15 cm. The height of the prism is 5 cm. Then, the total surface area of the prism is:
Option 1: 180 cm2
Option 2: 234 cm2
Option 3: 288 cm2
Option 4: 270 cm2
Question : If the area of the base of a cone is 154 cm2 and the area of its curved surface is 550 cm2, then its volume is:
Option 1: 1232 cm3
Option 2: 1122 cm3
Option 3: 1434 cm3
Option 4: 1535 cm3
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