Example 7
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy.(Take π = 3.14)
Now,
Volume of toy = Volume of cone + Volume of hemisphere
Volume of cone
Height of cone = OA = h = 2 cm
Diameter of cone = BC = 4 cm
So, Radius = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 "=" 4/2 = 2 cm
Now,
Volume of cone = 1/3 𝜋𝑟2ℎ
= 1/3 𝜋 × (2)2 × (2)
= 𝟖𝝅/𝟑 cm3
Volume of hemisphere
Diameter of hemisphere = BC = 4 cm
So, Radius = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 "=" 4/2 = 2 cm
Volume of hemisphere = 2/3 𝜋𝑟3
= 2/3×π×(2)3
= 2/3 π×2×2×2
= 𝟏𝟔𝝅/𝟑 cm3
Now,
Volume of the toy = Volume of cone + Volume of hemisphere
= 𝟖𝝅/𝟑+𝟏𝟔𝝅/𝟑
= (8𝜋 + 16𝜋)/3
= 2/3 π × 2 × 2 × 2
= 𝟏𝟔𝝅/𝟑 cm3
Now,
Volume of the toy = Volume of cone + Volume of hemisphere
= 𝟖𝝅/𝟑+𝟏𝟔𝝅/𝟑
= (8𝜋 + 16𝜋)/3
= 24𝜋/3
= (24 × 3.14)/3
= 8 × 3.14
= 25.12 cm3
Now, we need to find the difference of the volumes of the cylinder and the toy.
Volume of cylinder
Cylinder circumscribes the toy.
Diameter of cylinder = HG = BC = 4 cm
Radius = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 "=" 4/2 = 2 cm
And,
Height of cylinder = OA + OP
= Height of cone + Radius of hemisphere
= 2 + 2
= 4 cm
Now,
Volume of cylinder = 𝜋𝑟2ℎ
= 3.14×(2)2×(4)
= 3.14×4×4
= 50.24
Therefore,
Difference of the volume = Volume of cylinder – Volume of toy
= 50.24 – 25.12
= 25.12 cm3
Hence, difference of the volume is 25.12 cm3

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and 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!