A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform
Solution:
A figure is drawn below to visualize the shapes according to the given question.
The shape of the well will be cylindrical, and soil evenly spread out to form a platform will be in a cuboidal shape.
So, the volume of the soil dug from the well will be equal to the volume of soil evenly spread out to form a platform.
Volume of soil dug out from the well = Volume of soil used to make the platform
Hence, Volume of the cylindrical well = Volume of the cuboidal platform.
We will find the volume of the cylinder and cuboid by using formulae;
Volume of the cylinder = πr2h, where r and h are the radius and height of the cylinder respectively.
Volume of the cuboid = l × b × H, where l, b, and H are length breadth and height of the cuboid respectively.
Depth of the cylindrical well, h = 20 m
Radius of the cylindrical well, r = 7/2 m
Length of the cuboidal platform, l = 22 m
Breadth of the cuboidal platform, b = 14 m
Let the height of the cuboidal platform = H
Volume of the cylindrical well = Volume of the cuboidal platform
πr2h = lbH
H = πr2h / lb
= (22/7 × 7/2 m × 7/2 m × 20 m) / (22 m × 14 m)
= 5/2 m
= 2.5 m
Therefore, the height of the platform will be 2.5 m.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 3
Summary:
If a 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m, the height of the platform will be 2.5 m.
☛ Related Questions:
- A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
- A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
- How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
- A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.