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NCERT Class 10 Mathematics Solutions: Chapter 13- Areas and Volumes Exercise 13.3 Part 2

Illustration: 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:

The Shape of a Circular Ring

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.