Volume of a Sphere

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.
$\left[2Marks\right]$

Q.

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. The number of spheres formed will be

1. 600

2. 400

3. 800

4. 200

Q.

The surface area of a solid metallic sphere is $616c{m}^2$. It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained?

1. 96

2. 32

3. 64

4. 48

Q.

27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere.The radius of the single big sphere(in cm) is______.

1. 3 cm

2. 15 cm

3. 9 cm

4. 5 cm

Q.

A hemisphere is melted and used some part of it to make a right circular cone whose radius and height are equal to the radius of the hemisphere. The volumes of hemisphere and cone are in the ratio 4:1.

1. False
2. True

Q. Find the volume of a sphere of radius 5.6 cm.

1. $799c{m}^3$
2. $765.45c{m}^3$
3. $735.91c{m}^3$
4. $700c{m}^3$

Q. What is the formula for the volume of a sphere?

1. $V=3\pi r$
2. $V=\frac{4}{3}\pi r^3$
3. $V=\frac{2}{3}\pi r^2$
4. $V=2\pi r^2$

Q.

A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 ${cm}^3$, find the total surface area of the cone. (Take $\pi$ = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.

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1. 400$\pi$ ${cm}^2$

2. 500$\pi$ ${cm}^2$

3. 900$\pi$ ${cm}^2$

4. 600$\pi$ ${cm}^2$

Q.

Among a cylinder (of radius r and height h=r), a cone (of radius r and height h=r) and a sphere of radius r the __ will have the maximum volume.

Q.

Volume of a sphere is directly proportional to the __ of its radius.