A wooden box of dimensions 8 metre x 7 metre x6 metre is to carry rectangular boxes of dimensions 8 cm x 7 cm x6 cm. The maximum number of boxes that can be carried in 1 wooden box is

Correct Answer Is : 1000000

Solution Is : Volume of wooden box = (8 * 7 * 6) cu.m. = (8 * 7 * 6 * 100?3) cu.m. Maximum number of boxes = 8 * 7 * 6 * 100³/ 8 * 7 * 6 =1000000

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

Correct Answer Is : √2 : 1

Solution Is :

A rectangular piece of paper of dimensions 22 cm by 12 cm is rolled along its length to form a cylinder. The Volume ( in cu. Cm) of the cylinder so formed is

Correct Answer Is : 462

Solution Is : Paper is folded along the length. Circumference of the base = 22 cm, Height of cylinder = 12 cm 2 π r = 22 => 2 * 22/7 * r = 22 => r = 7/2 cm Volume of cylinder = π r² h 22/7 * 7/2 * 7/2 * 12 = 462 cu.cm.

A sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is R, the volume of the cylinder is

a)
b)
c)
d)

Correct Answer Is :

Solution Is : Height of cylinder = 2 R units Radius of base = R units Volume of cylinder = π R² h => π(R²) (2R) = 2 π R?3

Correct Answer Is : 30°

Solution Is :

Correct Answer Is : None of these

Solution Is :

The total surface area of a regular triangular pyramid with each edge of length 1 cm is

Correct Answer Is : √3 cm²

Solution Is : Total surface area = 4 x √3/4 x (1)² = √3 sq.cm

The number of paving stones each measuring 2.5 m x 2m required to pave a rectangular courtyard 30m long and 17.5m wide is

Correct Answer Is : 105

Solution Is : Number of paving stones = Area of courtyard / Area of a stone = 30x 17.5 / 2.5 x 2 = 105

The perimeter of a sheet of paper in the shape of a quadrant of a circle is 75 cm. Its area would be ( π = 22/7)

Correct Answer Is : 346.5 cm²

Solution Is :

The perimeter of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangles is 9 cm. Determine the corresponding side of the second triangle.

Correct Answer Is : 6 cm

Solution Is : If the required side be x cm, then 30/20 = 9/x => 3x = 9 x 2 => x = 9x2/3 = 6 cm