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A solid cylinder has a base of radius 14 cm and height 15 cm. 4 identical cylinders are cut from each base as shown in the given figure. Height of small cylinder is 5 cm. What is the total surface area (in cm2) of the remaining part?

A solid cylinder has a base of radius 14 cm and height 15 cm. 4 identical cylinders are cut from each base as shown in the given figure. Height of small cylinder is 5 cm. What is the total surface area (in cm2) of the remaining part? Correct Answer 3432

Radius of larger cylinder = 14 cm and height = 15 cm

Radius of smaller cylinders = 28/8 = 7/2 cm and height = 5 cm

When the cylinders are cut as given in the question, the curved surface area of the

Remaining part will increase and CSA of the smaller cylinders will add up. While base area Will decrease by area of one base and increase by area of another base of the smaller

Cylinders thus no increment in base area.

CSA of the remaining part = 2πrh + 8 × 2πr1h1 (∵ There are two bases(top + base) in a cylinder and according to question, 4 small cylinders are cut out from each base ∴ we multiplied it by 8)

⇒ 2 × 22/7 (14 × 15 + 8 × 5 × 7/2) 

⇒ 2 × 22/7 × 350

⇒ 2200 cm2

Total Base Area of remaining part = 2πr2 – 8πr12 + 8πr12

⇒ 2 × 22/7 × 196

⇒ 1232 cm2

Total surface area of the remaining part = 2200 + 1232 = 3432 cm2

TSA = 2πRH + 8 (2πrh)+(8πr2) + 2

= 2πRH + 16πrh  + 8πr2 +2πR2 - 8πr2

= 2π  

= 2π

= 28π

= 28 × 22/7 × 39 = 88 × 39

= 3432 cm2

So the total surface area of the remaining part = 3432cm2

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