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
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 cm
2
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 cm
2
$\therefore$ The total surface area of the remaining part = 2200 + 1232 = 3432 cm
2
Hence, the correct answer is 3432.
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