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?

18480 cm³

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