Question : If the inner radius of a hemispherical bowl is 5 cm and its thickness is 0.25 cm, find the volume of the material required to make the bowl. (Use $\pi = \frac{22}{7}$) (Rounded up to two decimal places).
Option 1: 34 cm3
Option 2: 44 cm3
Option 3: 45.34 cm3
Option 4: 41.28 cm3
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Correct Answer: 41.28 cm3
Solution : Volume of the hemispherical bowl = $\frac{2}{3} × \pi × (R^{3} - r^{3})$ Where, $r$ is the inner radius of the bowl = 5 cm And, $R$ is the outer radius of the bowl = (5 + 0.25) = 5.25 cm So, the volume $=\frac{2}{3} × \frac{22}{7} × [(5.25^{3}) - (5)^{3}]$ $=\frac{44}{21} × 19.70$ $= 41.28$ cm3 Hence, the correct answer is 41.28 cm3.
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Question : Steel is used to make a hemispherical bowl that is 0.37 cm thick. The bowl's inner radius is 6 cm. Find the bowl's outside curved surface area (take $\pi=\frac{22}{7}$).
Option 1: 532 cm2
Option 2: 255.0548 cm2
Option 3: 484 cm2
Option 4: 523.4107 cm2
Question : A hollow sphere has an outer radius of 6 cm and inner radius of 3 cm. What is the volume of this hollow sphere?
Option 1: 252$\pi$ cm3
Option 2: 356$\pi$ cm3
Option 3: 144$\pi$ cm3
Option 4: 175$\pi$ cm3
Question : The volume of a sphere of radius 4.2 cm is: (Use $\pi=\frac{22}{7}$)
Option 1: 278.234 cm3
Option 2: 312.725 cm3
Option 3: 297.824 cm3
Option 4: 310.464 cm3
Question : The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe (take $\pi=\frac{22}{7}$ ) correct to two places of decimal.
Option 1: 1,662.67 cm2
Option 2: 1,552.57 cm2
Option 3: 1,442.48 cm2
Option 4: 1,772.76 cm2
Question : The height of a cylinder is 6 cm more than the radius of its base. If its radius is 14 cm, then what will be the volume of this cylinder? (use $\pi=\frac{22}{7}$)
Option 1: 13,560 cm3
Option 2: 14,340 cm3
Option 3: 10,440 cm3
Option 4: 12,320 cm3
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