Q.1
If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their height will be :
Q.2
The volume of a sphere is $$2145\frac{{11}}{{21}}{\text{c}}{{\text{m}}^3}.$$   Its radius is equal to :
Q.3
The diameter of a spare is 8 cm. It is melted and drawn into a wire of diameter 3 mm. The length of the wire is :
Q.4
The external and internal diameters of a hemispherical bowl are 10 cm and 8 cm respectively. What is the total surface area of the bowl ?
Q.5
A closed aquarium of dimensions 30 m × 25 cm × 20 cm is made up entirely of glass plates held together with tapes. The total length of tape required to hold the plates together (ignore the overlapping tapes) is :
Q.6
A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. It volume is :
Q.7
A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical ball. The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is :
Q.8
A pyramid has an equilateral triangle as its base of which each side is 1 m. Its slant edge is 3 m. The whole surface are of the pyramid is equal to :
Q.9
A swimming pool 9 m wide and 12 m long and 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is :
Q.10
An aluminium sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be :
Q.11
The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is :
Q.12
A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is $$\frac{1}{4}$$ of its height. The surface area of the solid is :
Q.13
The height of a right circular cylinder is 6 m. If three times the sum of the areas of its two circular faces is twice the area of the curved surface, then the radius of its base is :
Q.14
It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :
Q.15
Which one of the following figures will generate a cone when rotated about one of its straight edges ?
Q.16
If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, what is the ratio of their volumes ?
Q.17
Consider the volumes of the following
1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm
The volumes of these in the decreasing order is :
Q.18
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to from a single sphere, the diameter of the new sphere will be :
Q.19
When a ball bounces, it rises to $$\frac{2}{3}$$ of the height from which it fell. If the ball is dropped from a height of 36 m, how high will it rise at the third bounce ?
Q.20
The sum of perimeters of the six faces of a cuboid is 72 cm and the total surface area of the cuboid is 16 cm2. Find the longest possible length that can be kept inside the cuboid :
Q.21
The surface area of a cube is 150 cm2. Its volume is :
Q.22
The dimensions of a cuboid are 7 cm, 11 cm and 13 cm. The total surface area is :
Q.23
Rita and Meeta both are having lunch boxes of a cuboid shape. Length and breadth of Rita's lunch box are 10% more than that of Meeta's lunch box, but the depth of Rita's lunch box is 20% less than that of Meeta's lunch box. The ratio of the capacity of Rita's lunch box to that of Meeta's lunch box is :
Q.24
If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes will be ?
Q.25
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
Q.26
The diameter of the base of a cylindrical drum is 35 dm and the height is 24 dm. It is full of kerosene. How many tins each of size 25 cm × 22 cm × 35 cm can be filled with kerosene from the drum ?
Q.27
A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is :
Q.28
A solid body is made up of a cylinder of radius r and height r, a cone of base radius r and height r fixed to the cylinder's one base and a hemisphere of radius r to its other base. The total volume of the body (given r = 2) is :
Q.29
The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity of 5 m/sec. How many minutes will it take in filling the cistern with water ?
Q.30
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
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