Question : The total surface area of a solid hemisphere is $942 \mathrm{~cm}^2$. Its volume (in $\mathrm{cm}^3$ ) is closest to: (Take $\pi=3.14$ )
Option 1: 2089
Option 2: 2093
Option 3: 2037
Option 4: 2097
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Correct Answer: 2093
Solution : Given: The total surface area of a solid hemisphere = $942\ cm^2$ $3 \pi r^2=942$ ⇒ $3\times 3.14\times r^2=942$ ⇒ $3.14\times r^2=314$ ⇒ $ r^2=100$ ⇒ $ r=10$ Volume of hemisphere = $\frac{2}{3}\pi r^3$ = $\frac{2}{3}\times 3.14\times10\times10\times10$ = $\frac{6280}{3}$ = $2093.33 \approx 2093$ cm3 Hence, the correct answer is 2093 cm3.
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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
Question : If the curved surface area of a cylinder is $126\pi$ cm2 and its height is 14 cm, what is the volume of the cylinder?
Option 1: $283 \frac{1}{2} \pi\ \mathrm{cm}^3$
Option 2: $137\frac{1}{2} \pi\ \mathrm{cm}^3$
Option 3: $128\frac{1}{2} \pi\ \mathrm{cm}^3$
Option 4: $125\frac{1}{2} \pi\ \mathrm{cm}^3$
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 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 solid right circular cylinder of height 8 cm is $392 \pi$ cm3. Its curved surface area (in cm2) is:
Option 1: $161 \pi$
Option 2: $96 \pi$
Option 3: $210 \pi$
Option 4: $112 \pi$
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