A well of radius 2.8 m is dug up to a depth of 15 m. The earth which is taken out is used to make a platform which is 7 m wide around the well in a circular shape. Find the height of the platform?
1. 1.33 m
2. 2.7 m
3. 4.3 m
4. 0.9 m
1. 1.33 m
2. 2.7 m
3. 4.3 m
4. 0.9 m
Correct Answer – Option 1 : 1.33 m
Given:
Radius of well = 2.8 m
Height of well = 15 m
Width of platform = 7 m
Concept:
The volume of the platform will be equal to the volume of the earth taken out, i.e. to the volume of cylindrical shaped well. The platform is also is in the shape of cylinder whose inner radius is the radius of the well and the outer radius will be the sum of radius of well and the thickness of the platform.
Formula used:
Volume of cylinder = πr2h
Volume of Hollow cylinder = π(R2 – r2)h
Where, ‘R’ is the outer radius and ‘r’ is inner radius.
Calculation:
Let, the height of the platform = h
‘r’ = radius of well
‘R’ = radius (Platform + well) = 7 + 2.8 = 9.8 m
∵ Volume of the well = Volume of the Cylindrical platform
∴ πr2h = π(R2 – r2)h
⇒ 2.8 × 2.8 × 15 = [(9.8)2 – (2.8)2] × h
⇒ 117.6 = (96.04 – 7.84) × h
⇒ 117.6 = 88.2 × h
⇒ h = 117.6/88.2
⇒ h = 4/3 = 1.33m