Question : A hemispherical bowl is made of 1 cm thick steel. The inside radius of the bowl is 4 cm. The volume of the steel (in cm3) used in making the bowl is:
Option 1: $40\frac{2}{3}\pi$
Option 2: $27\frac{1}{3}\pi$
Option 3: $41\frac{1}{3}\pi$
Option 4: $35\frac{1}{3}\pi$
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Correct Answer: $40\frac{2}{3}\pi$
Solution : Given: Inner radius $(r)$ = 4 cm Outer radius $(R)$ = 4 + 1 = 5 cm According to the question, The volume of steel used = $\frac{2}{3}×\pi (R^3-r^3)$ = $\frac{2}{3}×\pi (5^3-4^3)$ = $\frac{2}{3}×\pi (125-64)$ = $\frac{2}{3}×\pi ×61$ = $\frac{122}{3}×\pi$ = $40\frac{2}{3}\pi\ \text{cm}^3$ Hence, the correct answer is $40\frac{2}{3}\pi$.
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Question : A hemispherical bowl has an internal radius of 6 cm. The internal surface area would be: (Take $\pi =3.14$)
Option 1: 225 cm2
Option 2: 400 cm2
Option 3: 289.75 cm2
Option 4: 226.08 cm2
Question : If a right circular cone of height 24 cm has the circumference of its base 42$\pi$ cm, then the volume of the cone is: (Use $\pi=\frac{22}{7}$)
Option 1: 15211 cm3
Option 2: 11088 cm3
Option 3: 12034 cm3
Option 4: 21011 cm3
Question : Find the volume of a solid sphere whose diameter is 42 cm. (Use $\pi=\frac{22}{7}$)
Option 1: 38807 cm3
Option 2: 38808 cm3
Option 3: 38806 cm3
Option 4: 38805 cm3
Question : The total surface area of a cylinder whose radius is 6 cm and height is 8 cm is: (Use $\pi=\frac{22}{7}$)
Option 1: 528 cm2
Option 2: 575 cm2
Option 3: 658 cm2
Option 4: 625 cm2
Question : The perimeter of a minor sector of a circle of radius 5 cm is 15.5 cm. Find the area of the minor sector (use $\pi=\frac{22}{7}$ ).
Option 1: 17.53 cm2
Option 2: 13.75 cm2
Option 3: 13.57 cm2
Option 4: 17.35 cm2
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