### Aptitude - Mensuration Test

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To comfortably sit in a room, every girl must be allowed a floor space of 2 sq.m. and air space of 5.5 cubic metres.  Fifty girls are to be seated comfortably in a room 10m. long.  What should be its height?

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

A rectangle has width a and length b. If the width is decreased by 20% and the length is increases by 10%, then what is the area of the new rectangle in percentage compared to ’ab’ ?

Two diagonals of a parallelogram are 72 cm and 30 cm respectively. What is its perimeter?

If the area of a square increases by 69%, then the side of the square increases by

XYZ is an equilateral triangle with vertices X (6, -2), Y (2, - 1) and Z (4, -2). If ZA is one of its medians find the length of the median

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is

The ratio between rhe perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle ?

The coordinates of a point which divide the join of A (5, 5) and (8, 5) in the ratio 2 : 1 are

The circumference of a circle is 100 cm. The side of a square inscribed in the circle is:

XYZ is an equilateral triangle with vertices X (6, -2), Y (2, - 1) and Z (4, -2). If ZA is one of its medians find the length of the median

The points of intersection of the circle x2 +y2=34 and line y=5

If a wire is bent into the shape of a square, then the area of the square is 81sq.cm. When the wire is bent into a semi-circular shape, then the area of the semi-circle will be:

There are two concentric circles. The radius of the outer circle is 8.5 cm and the length of the longest chord of the outer circle that doesn't cut through the inner circle is 8 cm. What fraction of the bigger circle is not covered by the smaller circle?

The volume of the sphere Q is 3764% less than the volume of sphere P and the volume of sphere R is 1927 % less than that of sphere Q. By what % is the surface area of sphere R less than the surface area of sphere P?

The area of the triangle whose vertices are (a, a), (a + 1, a + 1), (a + 2, a) is :

What will be the cost of gardening  1metre broad boundary around a rectangular plot having perimeter of 340 meters at the   rate of Rs. 10 per square metres?

if the volume of a cube is 729 cm3, then the surface area of the cube will be

What is the slope of the line given by the equation 3w - 7 = 6 - 2y?

The radii of two cones are in the ratio 2:1, their volumes are equal. Find the ratio of their heights

The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will It cover in 5 revolutions use (π=22/ 7)

The distance between the points (-9, 5) and (-8, -20) is

The number of revolutions made by a wheel of diameter 56 cm in covering a distance of 1.1 km is: (use π= 22/7)

The area of a rhombus is 150 cm2. The length of one of its diagonals is 10cm. The length of the other diagonal is:

Find the co-ordinates of the foot of the perpendicular from point (5,7) on the line whose equation is: x + 7y - 10 = 0.

The number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 6m long , 5m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is

The height of the Qutub Minar is 230 metres. It is planned that a stairway from ground to the topof the Minar would be made by arranging cube shaped boulders in a step like fashion. A man firstplaces a boulder on the ground. He then steps on to it, and then throws one boulder down such thatit touches the side of the previous bolder, and then places one over the new one. He then climbsonto the last boulder thus placed and continues to do the same to create steps right to the top, witheach of his step being 1 metre. If each boulder measures 1 cubic metre, how many boulders arerequired in all ?

One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the parallelogram is:

If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100sq.cm. The sides of the rectangle are

There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

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