Ex 12.2, 5
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.
Number of lead shots = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑓𝑙𝑜𝑤𝑛 𝑜𝑢𝑡)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑙𝑒𝑎𝑑 𝑠ℎ𝑜𝑡)
Volume of water flown out
Volume of water flown out = 1/4 of volume of cone
Given
radius of cone = r = 5 cm
height of cone = h = 8 cm
Volume of cone = 1/3 𝜋𝑟^2 ℎ
= 1/3×22/7×5×5×8
= 4400/21 cm3
Volume of water flown out = 1/4 × Volume of cone
= 1/4 × 4400/21 = 1100/21 cm3
Volume of 1 lead shot
Lead shot is in from of sphere with
Radius = r = 0.5 cm
Volume of 1 lead shot = Volume of sphere
= 4/3 πr3
= 4/3×22/7×(0.5)3
= 11/21 cm3
Now,
Number of lead shots = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑓𝑙𝑜𝑤𝑛 𝑜𝑢𝑡)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑙𝑒𝑎𝑑 𝑠ℎ𝑜𝑡)
= (1100/21)/(11/21)
= 1100/21 × 21/11
= 100
Hence there are 100 such lead shots.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!