Instructions

For the following questions answer them individually

Question 71

A well of 4m diameter and 35m deep is dugout and the excavated soil is transported in a rectangular parallelopiped shaped truck with dimensions $$5m\times2m\times0.5m$$. To avoid over during transportation only 80% of its capacity is filled. If the loose soil occupies 20% more space while filling into the truck, then the number of trips required to transport the soil completely away from the place of digging is

Question 72

If the volumes of a sphere and a cube are in the ratio $$9\pi$$ : 2, then the ratio of the radius of the sphere to the edge of the cube is

Question 73

The dimensions of a rectangular plot is $$40m\times20m$$. A path is formed across the plot along the length and breadth with a uniform width of 2 meters. If the cot of forming, the path is Rs. 500 per sq.meter, the cost of laying that path (in Rs.) is

Question 74

A person packs sweets boxes of dimensions $$15cm\times15cm\times15cm$$ in a basket of size $$120cm\times120cm\times120cm$$. If he now wants to carry the maximum number of cubical boxes having the maximum integer dimensions but less than the dimensions of the earlier boxes without leaving any space unused, the number of such boxes he can carry is

Question 75

From a circle of radius 12cm centered at O, a sector OAB of are length $$8\pi$$ cm is cut and from it a cone is formed by joining OA and OB. If the volume of the cone is V cubic cm and its lateral surface area is S square cm, then V:S =

Question 76

A solid sphere of radius $$r$$ is melted and with that material a solid cone and twenty two identical solid cubes were made. If the height of cone and edge of each cube are each equal 9 to half the radius of the sphere, then the ratio of the radius of the cone to its height is

Question 77

What is the area (in sq. cms) of the shaded portion of the following diagram in which each side of the triangle is 14 cms and its vertices being the centres of three mutually touching circles?

Question 78

Let $$\triangle$$ be the area of the circumcircle of a right angled triangle ABC with $$\angle B$$ = 90**Â°**. Let $$\triangle_1 and \triangle_2$$ be areas of the two circle with diameters BC and BA respectively. Then

Question 79

From each of the corners of a rectangular sheet of dimensions $$36cm\times24cm$$, a small square of dimensions $$4cm\times4cm$$ is removed. If the edges on the four sides are folded and a box is formed then the volume of the box so formed (in cm3)

Question 80

In a square of side 8 cm, 5 identical circles are placed as shown in the figure. Then the radius (in cms) of each of the circle is

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