Question : The largest sphere is carved out of a cube of side 7 cm. The volume of the sphere will be:
Option 1: 179.67 cm3
Option 2: 165.67 cm3
Option 3: 175.67 cm3
Option 4: 182.67 cm3
Correct Answer: 179.67 cm3
Solution : The diameter of the sphere is equal to the side of the cube. d = 7 cm r = $\frac{7}{2}$ cm The volume of a sphere $= \frac{4}{3}\pi r^3$ $V = \frac{4}{3}\pi \left(\frac{7}{2}\right)^3 = \frac{4×22}{3×7}× \frac{343}{8} = 179.67$ Hence, the correct answer is 179.67 cm3.
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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
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 : If the volume of a sphere is 4851 cm3, then its surface area (in cm2)is: $\left(\right.$Take $\pi=\frac{22}{7})$
Option 1: 1427
Option 2: 1386
Option 3: 1399
Option 4: 1268
Question : The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take $\pi$ = 3.14).
Option 1: 3391.2 cm2
Option 2: 5391.2 cm2
Option 3: 4391.2 cm2
Option 4: 5591.2 cm2
Question : The volume of a sphere is given by 130977 cm3. Its surface area (in cm2) is:
Option 1: 16847
Option 2: 12474
Option 3: 17424
Option 4: 14274
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