Volume of Spherical Shell

Q.

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is:

1. $\sqrt{3}cm$

2. $2cm$

3. $3cm$

4. $4cm$

Q.

A right circular cone is $5.4cm$ high and the radius of its base is $2cm$.

It is melted and recast into another right circular one with a radius of base as $1.5cm$. find the height of the new cone formed.

Q.

The outer and inner diameters of a spherical shell are $10cm$and $9cm$respectively. Find the volume of metal contained in it. (Take $\mathrm{\pi }=\frac{22}{7}$)

Q.

Question 2 (ii)
Find the surface area of a sphere of diameter:

(ii) 21 cm

$[Assume\pi =\frac{22}{7}]$

Q.

A vapor cone is a cloud of condensed water that forms when an aircraft breaks the sound of condensed water that forms when an aircraft breaks the sound barrier. How does doubling both the diameter and the highest affect the volume of the vapor cone ?

Q. Find the radius of sphere whose surface area is $154c{m}^2$.

Q. How many spherical balls can be made out of a solve cube of lead whose edge measure $44cm$ and each ball being $4cm$ in diameter.

Q. Write the formula to find volume of spherical shell.

Q. 12.The product and difference of inner and outer radiusof a hemi-spherical shell are 12 cm2 and 1 cmrespectively. The sum of inner and outer surfaceareas of the shell i equal to

Q. In TSA of spherical shell, why is it not needed to add 4π(r)^2 + 4π(R)^2? Why only 4π(R)^2 is written?

Q. A hollow spherical shell has inner diameter $4$ cm and outer diameter $8$ cm. Determine the volume of the shell.

1. $204.45c{m}^3$
2. $134.45c{m}^3$
3. $334.45c{m}^3$
4. $234.45c{m}^3$

Q. A solid cylinder of glass, the inner radius is $9$ cm and the outer radius is $12$ cm. Find the approximate volume of the sphere.

1. $\approx 1000c{m}^3$
2. $\approx 2000c{m}^3$
3. $\approx 3000c{m}^3$
4. $\approx 4000c{m}^3$

Q. A spherical shell 5 m thick has an outer radius of 7 m. What is the volume of shell?

1. $1302.53m$
2. $1202.53m$
3. $1102.53m$
4. $1402.53m$

Q. The radii of two solid metallic spheres are $r_1$ and $r_2$. The spheres are melted together and recast into a solid cone of height $(r_1+r_2)$. Show that the radius of the cone is $2\sqrt{r_1^2+r_2^2-r_1{r}_2}$.

Q. A spherical shell has a outer radius $14$ m and inner radius $7$ m. What's the volume of the sphere?

1. $\approx 9000m^3$
2. $\approx 8000m^3$
3. $\approx 10000m^3$
4. $\approx 7000m^3$

Q. What is the volume of material that is needed to form a spherical shell whose outer radius is $5$ ft and whose inner radius is $3$ ft?

1. $610.293f{t}^3$
2. $510.293f{t}^3$
3. $450.293f{t}^3$
4. $410.293f{t}^3$

Q. A hemispherical bowl of internal diameter $36$ cm is filled with some liquid. This liquid is to be filled into Cylinder shaped bottles each of radius $3$ cm and height $6$ cm. Find the number of bottles required to empty the bowl.

Q. Calculate the volume of the shell. A hollow spherical shell has inner radius $0.3$ cm and outer radius $0.5$ cm.

1. $0.310c{m}^3$
2. $0.410c{m}^3$
3. $0.110c{m}^3$
4. $0.210c{m}^3$

Q. Find the volume of material that is needed to form a spherical shell whose outer radius is $3.0$ inches and whose inner radius is $0.1$ inches.

1. $103.035i{n}^3$
2. $93.035i{n}^3$
3. $123.035i{n}^3$
4. $113.035i{n}^3$

Q. A juice seller was serving his customers using glass. The inner diameter of the cylindrical glass was $5cm$, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was $10cm$, find what the apparent capacity of the glass was and what the actual capacity was (Use $\pi =3.14$)

Q. The diameters of internal and external surfaces of a hollow spherical shell are $10cm$ and $6cm$ respectively. If it is melted and recast into a solid cylinder of length of $2\frac{2}{3}cm$, find the diameter of the cylinder.

Q. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Q. The inner diameter of the spherical shell is $12$ mm and outer diameter is $24$ mm. Find the volume of the shell.

1. $6330m{m}^3$
2. $5330m{m}^3$
3. $4330m{m}^3$
4. $3330m{m}^3$

Q. ntThree concentric spherical shells have radii a, b, c respectively (a