A cylindrical vessel with internal diameter 10 cm and height 10.5 cm i

1.	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» 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

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»

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