Exercise 16.1

Rain water, which falls on a flat rectangular surface of length 6m and breadth 4m is transferred into a cylindrical vessel of internal radius 20 cm .What will be the height of water in the cylindrical vessel if a rainfall of 1cm has fallen?

According to the question, Length of the rectangular surface $=6m=600cm$ Breadth of the rectangular surface $=4m=400cm$ Height of the perceived rain $=1cm$ Then, Volume of the rectangular surface...

read more

A cylindrical bucket, 32cm high and 18cm of radius of the base, 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 24cm, find the radius and slant height of the heap.

It is given in the question that, Height of the cylindrical bucket $=32cm$ Radius of the cylindrical bucket $=18cm$ Height of conical heap $=24cm$ As we know that, Formula for volume of cylinder...

read more

A cylindrical bucket, 32cm high and 18cm of radius of the base, 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 24cm, find the radius and slant height of the heap.

It is given that, Height of the cylindrical bucket $=32cm$ Radius of the cylindrical bucket $=18cm$ Height of conical heap $=24cm$ As we know that, Volume of cylinder $=\pi \times {{r}^{2}}\times h$...

read more

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

Assume the radius of the big ball be $xcm$ The radius of the small ball $=x/4cm$ Let the number of balls $=n$ Then according to the question, we have Volume of n small balls $=$ Volume of the big...

read more

The diameter of a metallic sphere is equal to 9cm. It is melted and drawn into a long wire of diameter 2mm havinThe diameter of a metallic sphere is equal to 9cm. It is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire.g uniform cross-section. Find the length of the wire.

According to the question it is given that, Radius of the sphere $=9/2cm$ Its volume will be $=4/3\pi {{r}^{3}}=4/3\pi {{\left( 9/2 \right)}^{3}}$ Then, the radius of the wire $=2mm=0.2cm$ Assume...

read more

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of the cylindrical vessel?

It is given that, The diameter of the cylinder $=$ the height of the cylinder $⇒h=2r$, where h – height of the cylinder and r – radius of the cylinder As we know that, Volume of a cylinder $=\pi...

read more