A cylindrical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
(A) 12 cm
(B) 24 cm
(C) 36 cm
(D) 48 cm
The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is
(A) 2 : 3
(B) 3 : 2
(C) 9 : 4
(D) 4 : 9
The number of coins of radius 0.75 cm and thickness 0.2cm required to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is:
(A) 500
(B) 600
(C) 460
(D) 640
How many hemispherical balls can be made from a cylinder 56 cm high and 12 cm diameter, when every ball being 0.75 cm in radius?
(A) 1792
(B) 3584
(C) 4824
(D) 7168
On a rainy day, 60 cm of rain is recorded in a region. What is the volume of water collected in an open and empty rectangular water tank that measures 12 m (length) ×10 m (width) and 50 cm (depth)?
(A)
120 m3
(B)
72 m3
(C)
60 m3
(D)
48 m3
If 15 August 2001 was Wednesday, then what was the day of the week on 2 October 2001?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
The radius of a wire is decreased to one third. If volume remains the same, length will increase by :
(A) 6 times
(B) 1 time
(C) 3 times
(D) 9 times
The volume of a right rectangular pyramid is 220 m3. What is the height of the pyramid, if the area of its base is 55 m2?
(A) 8 metre
(B) 13.5 metre
(C) 12 metre
(D) 9 metre
A prism with a right triangular base is 25 cm high. If the shorter sides of the triangle are in the ratio of 1 : 2 and the volume of the prism is 100 cm3 , what is the length of the longest side of the triangle?
(A) √5 cm
(B) 2√5 cm
(C) 5√2 cm
(D) 5 cm
The ratio of the volume of a cube to that of a sphere which will fit inside the cube is
(A) 4 : π
(B) 4 : 3π
(C) 6 : π
(D) 2 : π
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