A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel
Solution:
The figure drawn below of the vessel and lead shot is to visualize it.
As the water is filled up to the brim in the vessel
Volume of water in the vessel = Volume of the conical vessel
On dropping a certain number of lead shots (sphere) into the vessel one-fourth of the water flows out.
Volume of all lead shots dropped into the vessel = 1/4 × Volume of the water in the vessel
Hence,
Number of lead shots = 1/4 × volume of the water in the vessel ÷ volume of each lead shot
We will find the volume of the water in the vessel and lead shot by using formulae;
Volume of the sphere = 4/3 πr3
where r is the radius of the sphere
Volume of the cone = 1/3 πR2h
where R and h are the radius and height of the cone respectively
Height of the conical vessel, h = 8 cm
Radius of the conical vessel, R = 5 cm
Radius of the spherical lead shot, r = 0.5 cm
Number of lead shots = 1/4 × volume of the water in the vessel ÷ volume of each lead shot
= 1 /4 × (1/3) πR2h × 3/4 πr3
= πR2h/12 × 3/4πr3
= R2h / 16r3
= (5cm × 5 cm × 8 cm) / (16 × 0.5 cm × 0.5 cm × 0.5 cm)
= 100
Thus, the number of lead shots dropped in the vessel is 100.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 Question 5
Summary:
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. The number of lead shots dropped in the vessel are 100
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