Question : The volume of a solid hemisphere is 19,404 cm3. Its total surface area (in cm2) is: (Take $\pi=\frac{22}{7}$)
Option 1: 2772
Option 2: 3465
Option 3: 2079
Option 4: 4158
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Correct Answer: 4158
Solution : Let $r$ be the radius of the hemisphere. Volume of a hemisphere, V = $\frac{2}{3} \pi r^3$ Given: V = $19404$ ⇒ $19404 = \frac{2}{3} \pi r^3$ ⇒ $19404 = \frac{2}{3}\times \frac{22}{7}\times r^3$ ⇒ $r^3= 9261$ ⇒ $r = 21\ \text{cm}$ Total Surface Area of the hemisphere = $3 \pi r^2=3 \times \frac{22}{7} \times 21^2= 4158\ \text{cm}^2$ Hence, the correct answer is 4,158 cm2.
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Question : The curved surface area of a solid hemisphere is 22 cm2. What is the total surface area of the hemisphere? (use $\pi=\frac{22}{7}$)
Option 1: 66 cm2
Option 2: 44 cm2
Option 3: 33 cm2
Option 4: 30 cm2
Question : The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$ )
Option 1: 572 cm2
Option 2: 528 cm2
Option 3: 660 cm2
Option 4: 616 cm2
Question : The volume of a solid hemisphere is 19404 cm3. Its total surface area is:
Option 1: 4158 cm2
Option 2: 2858 cm2
Option 3: 1738 cm2
Option 4: 2038 cm2
Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm2. If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)
Option 1: 2060 cm3
Option 2: 2480 cm3
Option 3: 3080 cm3
Option 4: 2760 cm3
Question : If the surface area of a sphere is $1386 \mathrm{~cm}^2$, then its volume is: (Take $\pi=\frac{22}{7}$ )
Option 1: 8451 cm3
Option 2: 4851 cm3
Option 3: 5418 cm3
Option 4: 4581 cm3
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