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NCERT Class 10 Mathematics Solutions: Chapter 13- Areas and Volumes Exercise 13.3 Part 2
1. A well of diameter is dug deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width to form an embankment. Find the height of the embankment.
Answer:
Shape of the well will be cylindrical.
Depth () of well
Radius () of the circular end of well
Width of embankment
Radius of well with embankment and inner radius
Consider, the height of embankment be .
Volume of soil dug from well = Volume of earth used to form embankment
So, the height of the embankment will be .
2. A container shaped like a right circular cylinder having diameter and height is full of ice cream. The ice cream is to be filled into cones of height and diameter , having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Answer:
Height () of cylindrical container
Radius () of circular end of container
Radius () of circular end of ice-cream cone
Height () of conical part of ice-cream cone
Consider ice-cream cones be filled with ice-cream of the container.
Volume of ice-cream in cylinder (Volume of 1 ice-cream cone + Volume of hemispherical shape on the top)
So, ice-cream cones can be filled with the ice-cream in the container 7.