Question

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder. (ii) left in the cylinder.(Take π = \(\frac{22}7\)

Answer 1

Given 

internal radius (r1) = \(\frac{10}2\) = 5 cm 

Height of cylindrical vessel (h) = 10.5 cm 

Outer radius of cylindrical vessel (r2) = \(\frac{7}2\) = 3.5 cm 

Length of cone (l) = 6 cm 

(i) Volume of water displaced = Volume of cone 

Volume of cone = \(\frac{1}3\)πr²l

= \(\frac{1}3\)π(3.5)² x 6

= 76.9 cm³ 

≈ 77 cm³ 

Volume of water displayed = 77 cm³ 

Volume of cylinder = πr²h 

= π(5)²10.5 

= 824.6 

≈ 825 cm³

(ii) Volume of water left in cylinder = Volume of cylinder – Volume of cone 

= 825 -77 = 748 cm³