Question : A solid cylinder has a radius of base of 14 cm and a height of 15 cm. Four identical cylinders are cut from each base, as shown in the given figure. The height of a small cylinder is 5 cm. What is the total surface area (in cm2) of the remaining part?
Option 1: 3740
Option 2: 3432
Option 3: 3124
Option 4: 2816
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Correct Answer: 3432
Solution : Radius of larger cylinder, $r$ = 14 cm and height, $h$= 15 cm Radius of smaller cylinders, $r_1$ = $\frac{28}{8}$ = $\frac{7}{2}$ cm and height, $h_1$ = 5 cm The curved surface area of the remaining part = $2\pi rh+8×2\pi r_1 h_1$ ($\because$ There are two bases (top + base) in a cylinder and according to the question, 4 small cylinders are cut out from each base. so, we multiplied it by 8) = 2 × $\frac{22}{7}$ × (14 × 15 + 8 × 5 × $\frac{7}{2}$) = 2 × $\frac{22}{7}$ × 350 = 2200 cm2 Total Base Area of remaining part = $2\pi r^2-8\pi r_1^2+8\pi r_1^2$ = 2 × $\frac{22}{7}$ × 196 = 1232 cm2 $\therefore$ The total surface area of the remaining part = 2200 + 1232 = 3432 cm2 Hence, the correct answer is 3432.
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Option 1: 2060 cm3
Option 2: 2480 cm3
Option 3: 3080 cm3
Option 4: 2760 cm3
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Option 1: 4740 cm3
Option 2: 4850 cm3
Option 3: 5390 cm3
Option 4: 4420 cm3
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Option 1: 224.65 cm3
Option 2: 194.72 cm3
Option 3: 324.86 cm3
Option 4: 261.95 cm3
Question : The radius of a right circular cylinder is four times its height. If the height of the cylinder is 14 cm, then what is the volume of the cylinder?
Option 1: 15468 cm3
Option 2: 14262 cm3
Option 3: 137984 cm3
Option 4: 11296 cm3
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Option 1: 13,560 cm3
Option 2: 14,340 cm3
Option 3: 10,440 cm3
Option 4: 12,320 cm3
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