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
Correct Answer: 1386
Solution : Given: The volume of the sphere of radius $r$ = 4851 cm3 We know, Volume of the sphere $=\frac{4}{3} ×\pi r^3$ ⇒ $4851 = \frac{4}{3} × \frac{22}{7} × r^3$ ⇒ $r^3= 4851 × \frac{21}{88}$ ⇒ $r^3= 441 × \frac{21}{8}$ ⇒ $r = \frac{21}{2}$ Also, Surface area of sphere = $4 × \pi r^2$ = $4 × \frac{22}{7} × (\frac{21}{2})^2$ = $4 × \frac{22}{7} × \frac{441}{4}$ = $22 × 63$ = $1386$ cm2 Hence, the correct answer is 1386 cm2.
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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 : The radius and height of a right circular cone are in the ratio 1 : 2.4. If its curved surface area is 2502.5 cm2, then what is its volume? (Take $\pi=\frac{22}{7}$)
Option 1: 8085 cm3
Option 2: 8820 cm3
Option 3: 11550 cm3
Option 4: 13475 cm3
Question : The ratio of the radius of the base and the height of a solid right circular cylinder is 2 : 3. If its volume is 202.125 cm3, then its total surface area is: (Take $\pi=\frac{22}{7}$)
Option 1: 192.5 cm2
Option 2: 154 cm2
Option 3: 168 cm2
Option 4: 115.5 cm2
Question : The curved surface area of a solid cylinder of height 15 cm is 660 cm2. What is the volume (in cm3) of the cylinder? $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
Option 1: 2060
Option 2: 2540
Option 3: 2310
Option 4: 3210
Question : The radius of the base of a cylinder is 14 cm and its curved surface area is 880 cm2. Its volume (in cm3) is: (Take $\pi=\frac{22}{7}$)
Option 1: 3080
Option 2: 1078
Option 3: 6160
Option 4: 9240
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