Volume of a sphere

Q.

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq. cm [Use $\pi =3.14$]

Q.

2 spheres of same metal weigh 1 kg and 7 kg. The radius of smaller sphere is 3 cm. The 2 spheres are melted to form a big sphere. Find diameter of new sphere.

Q.

A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm. [4 MARKS]

Q. The ratio of volume and total surface area of a solid sphere is 8 : 1, then value of radius = cm.

1. 2
2. 24
3. 64

Q. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire. [4 MARKS]

Q. Question 11
16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions $16cm\times 8cm\times 8cm$ and then the box is filled with water. Find the volume of water filled in the box

Q. Three solid spheres of gold whose radii are $1$ cm, $6$ cm and $8$ cm, respectively are melted into a single solid sphere. Find the radius of the sphere.

Q.

A solid metallic hemisphere of radius $8cm$ is melted and recasted into a right circular cone of base radius $6cm.$ Determine the height of the cone.

Q. The value of radius for which the numerical value of total surface area of a sphere and the volume of sphere are equal, will be:(Consider the units of volume and surface area as ${cm}^3\text{and}{cm}^2$)

1. $1cm$
2. $2cm$
3. $3cm$
4. $4cm$

Q. A hollow sphere of external and internal diameters of $8cm$ and $4cm$ respectively is melted and made into another solid in the shape of a right circular cone of base diameter $8cm$. Find the height of the cone.

Q. If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is

1. 100 $\pi$
2. 75 $\pi$
3. 60 $\pi$
4. 50 $\pi$

Q. The volumes of two spheres are in the ratio of $64:27$. The ratio of their surface areas is __________.

1. $2:3$
2. $9:16$
3. $16:9$
4. $1:2$

Q. If a sphere of radius $6cm$ is melted and drawn into a wire of radius $0.02cm$ then what is the length of the wire ?

Q. The volume of a cone is equal to that of a sphere. If the diameter of the base of cone is equal to the diameter of the sphere, what is the ratio of the height of the cone to the diameter of the sphere

1. $2:1$
2. $1:2$
3. $3:1$
4. $4:1$

Q. The radius of a solid sphere is $24cm$. It is melted and drawn into a long wire of uniform cross section. Find the length of the wire if its radius is $1.2mm$.

1. $12.8km$
2. $128km$
3. $1.8km$
4. None of these

Q. The decorative block shown in the figure is made of two solids, a cube, and a hemisphere. The base of the block is a cube with edge $5cm$ and the hemisphere fixed on the top has a diameter of $4.2cm$. Find the total surface area of the block. (Take $\pi =\frac{22}{7})$

Q. If the volume of sphere and cone are equal with same radius$\left(r\right)$ then calculate height$\left(h\right)$ of the cone.

1. $h=2r$
2. $h=4r$
3. $h=\frac{r}{2}$
4. $h=r$

Q. Small pebbles are continuously being added to a graduated cylindrical container containing water. The total volume of water and pebbles can be represented by the equation $V=24\pi +x\left(\frac{4}{3}\pi r^3\right)$, if the pebbles are considered to be spheres of radius $r$. If the volume of the graduated cylinder is $96\pi$ cubic centimetres, then, what is the maximum number of pebbles with a radius of $3$ centimetres that can be added without the volume of the fluid exceeding that of the graduated cylinder?

1. $2$
2. $1$
3. $4$
4. $3$

Q. 17.A ball of silver 4cm is covered with gold. If the volume of gold & silver are equal , then the thickness of gold is A) 2cm B)1.038 cm C)0.519cm D) 0.5038cm

Q. The radius of a solid sphere is $7$ cm. If the solid sphere is melt to form small spheres of radius $3.5$ cm. Then how many small spheres can be formed?

Q. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm${}^3)$ is needed to fill this capsule ?

1. $21.458m{m}^3$
2. $22.458m{m}^3$
3. $22.548m{m}^3$
4. None of these

Q.

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

Q. The diameter of an iron sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Q. From a solid cube of side $7$ cm, a conical cavity of height $7$ cm and radius $3$ cm is hollowed out. Find the volume of the remaining solid.

Q. Question 2
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions $9cm\times 11cm\times 12cm$ ?

Q. The number of spherical bullets each $0.6$ cm in diameter be made out of a rectangular solid $9$ cm $\times$ $11$ cm $\times 12$ cm is __________.

1. $10200$
2. $10250$
3. $10500$
4. $10550$

Q. A sphere of radius $r$ lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of $r$.

1. $r^3$
2. $2r^3$
3. $4r^3$
4. $\frac{4}{3}\pi r^3$
5. $8r^3$

Q. The internal and external radii of a hollow sphere are $3cm$ and $5cm$ respectively. The sphere is melted to form a solid cylinder of height $2\frac{2}{3}cm.$ Find the diameter and curved surface area of the cylinder.

Q. A tent is in the form of a right circular cylinder, surmounted by a cone. The diameter of the cylinder is $24$ m. The height of the cylindrical portion is $11$ m, while the vertex of the cone is $16$ m above the ground. Find the area of the canvas required for the tent is

1. $1320m^2$
2. $3120m^2$
3. $2130m^2$
4. $1230m^2$

Q. A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then.

1. $H=2R$
2. $H=3R$
3. $H=\sqrt{3}$R
4. $H=\frac{2}{3}$R