A solid cylinder has radius of base 21 cm and height 15 cm. 3 identical cylinders are cut from its base as shown in the given figure. Height of small cylinder is 5 cm. What is the volume (in cm³) of the remaining part?
Answer & explanation
Correct answer: option 4
Radius of bigger cylinder (R) = 21 cm
Height of bigger cylinder (H) = 15
Radius of one small cylinder (r) = \(\frac{21}{3}\) = 7 cm
Height of one small cylinder (h) = 5 cm
Volume of the remaining part = (Volume of bigger cylinder) - (Volume of 3 smaller cylinders)
= \(\pi \) (R)² x H - 3 x \(\pi \) (r)²x h
= \(\pi \) (21)² x 15 - 3 x \(\pi \) (7)²x 5
= \(\pi \) x 15 {(21)² - (7)²}
= \(\pi \) x 15 {(21 + 7) (21 - 7)}
= \(\frac{22}{7}\) x 15 x 28 x 14
= 18480 cm³