# Mensuration-42

### From Homeworkwiki

**A cylindrical cistern whose diameter is 14 cm is partially filled with water. If a conical block of iron**

**whose radius of the base is 3.5 cm and height 6 cm is wholly immersed in the water, by how much will the water level rise ?**

**Solution:** For cone, r = 3.5 cm = 7/2 cm, h = 6 cm

Volume of cone = 1/3 x Π r^{2} h = 1/3 x 22/7 x 7/2 x 7/2 x 6 = 77 cm^{3} -------- (1)

Radius of the cistern = 14/2 cm = 7 cm. Let the water level rise to h cm. Then

Volume of water in the cistern = Π r^{2} h = (22/7 x 7 x 7x h) cm^{3} ----------- (2)

From (1) and (2), we have

22/7 x 7 x 7 x h = 77

=> h = (77 x 7) / (22 x 7 x 7) = 1/2 = 0.5

Hence, the water level will rise to a height of 0.5 cm