Shape conversion of solids

Q.

A metallic sphere of radius $4.2cm$ is melted and recast into the shape of a cylinder of radius $6cm$. Find the height of the cylinder.

Q.

A rectangular tank with a square base, an open top, and a volume of $4000{\mathrm{ft}}^3$ is to be constructed of sheet steel.

Find the dimensions of the tank that has the minimum surface area.

The dimensions of the tank with minimum surface area are ____?? ft.

Q.

Question 1
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Q.

A cone of height h cm and base radius r cm is reshaped into a sphere. Then, which of the following is always correct?

1. Volume of cone = Volume of Sphere

2. Surface Area of Cone = Surface Area of Sphere

3. Radius of sphere = Radius of base of cone + Height of cone

4. Can’t Say anything about the volume or surface area relation

Q.

The are small metal pieces each 1 cm long. ‘L’ number of metal pieces are put together to form a long thin rod. What is the length of the rod in cm?

1. $\frac{L}{2}$

2. 1

3. L

4. 2L

Q. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Q. A well of height 30 m and radius 14 m is dug out. The sand extracted is used to make a platform of length 10 m, breadth 14 m and height H. What is the value of H?

1. 150 m
2. 180 m
3. 130 m
4. 132 m

Q. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Q. The base radius and height of a right circular solid cone is 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the numbers of spheres so formed.

1. 20
2. 64
3. 32
4. 16

Q. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.