- There is a solid iron pillar in front of Anowar’s house whose lower position is right circular cylindrical shaped and upper portion is cone-shaped. The length of their base diameter is 20 cm and the height of the cylindrical portion is 2.8m. and the height of conical portion is 42cm. if the weight of the one cm2 from is 7.2 gm., then let us calculate the weight of iron pillar.
2. The height of a solid right circular cone is 20 cm and its slant height is 25cm. If the height of a solid right circular cylinder, having as much volume as that of the cone, is 15cm, then let us calculate the base diameter of the cylinder.
3. There is some water in a right circular cylindrical can with the diameter of 24cm. if 60i solid conical iron pieces with base diameter of 6cm. and height of 4 cm are immersed completely into water, then let us write by calculating, the increased height of water level.
4. If the ratio of the curved surface areas of the solid cone and a solid right circular cylinder having some base rasii and some height in 5.8, then let us determine the ratio of their base radii and height.
5. By melting a solid iron sphere with 8cm radius, how many marble balls of 1 cm, diameter can be obtained-let us write by calculating it.
6. The base radius of a solid right circular iron rod is 32 cm and its length is 35 cm. Let us calculating the member of solid cones of 8 am radius and 28 cm height can be made by melting this rod.
7. Let us determine the volume of a solid right circular cone which can be made from a solid wooden cube of 4.2 dcm edge length by wasting minimum quantity of wood.
8. If the radii and the volume of a solid sphere and a solid right circular cylinder are equal then let us calculate the ratios and height of the cylinder.
9. Let us determine the number of solid spheres with diameter of 2.1dcm can be made by melting a solid copper rectangular parallelopiped piece with length of 6.6.dcm breadth of 4.2dcm and thickness of 1.4dcm and also calculate the quantity of metal in dcm in each sphere.
10. Let us determine the length of a right circular rod of 2.8cm radius made by recasting a solid gold sphere of 4.2cm radius.
11. If a solid silver sphere of a diameter of 6dxm is melted and recasted into a solid right circular rod, then let us determine the length of diameter of the rod.
12. The length of the radius of cross-section of a solid right circular rod is 3.2dcm. By melting the rod 21 solid spheres are made, if the radius of the sphere is 8cm, then let us determine the length of the rod.
13. Half of a tank of 21dcm. length 11dcm, breadth and 6dcm, depth is full of water. Now of 100 iron spheres of 21cm diameter is immersed completely into the water of the tank, the let us calculate the rise of water level in dcm.
14. Let us determine the ratio of volumes of a solid cone, a solid hemisphere and a solid cylinder of same base diameter and same height.
15. The external radius of a hollow sphere made of lead sheet of 1cm, thickness I 6cm. If melting the sphere, a solid a right circular rod of 2cm. radius Is made, then let us calculate the length of the rod.
16. The cross-section of a rectangular parallelopiped
wooden log of 2m. length is a square and each of its side is 14 dcm in length.
If this log can be converted into a right circular log by wasting minimum
amount of wood, then let us calculate what amount of wood (in m2)
will be remained in it and what amount of wood (in m3) will be wasted.
[ Hints : The circumcircle inscribed in a rectangular
figure, the length of the diameter of the circle is equal to the length of the
side of the square.]