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TEST OF INTEGRATION XII 1 HR 30 MARKS TOMORROW …..

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A cone is 24 cm high and 15.75

1. A cone is 24 cm high and 15.75 cm in radius. If it is melted and recast into smaller cones, each is 5.25 cm in diameter and 6 cm high, how many such cones can be made?
2. The radius and height of a right circular cone are 9 cm and 36 cm respectively. Another cone is 54 cm high and the diameter of the base is 24 cm. Both the cones are melted together and recast into a cylinder whose base radius is 9 cm. Find the height of cylinder.
3. A cylinder is 12 cm high and the radius of its base is 6 cm. Another cylinder is 18 cm high and the radius of the base is 8 cm. Both the cylinder are melted together and recast into a right circular cone with height 33 cm. Find the diameter of  the base of the cone.

TRIG TEST

1. Find a point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3).
2. Find the value of x for which the distance between the point P(2, -3) and Q(x, 5) is 10 units.
3. The coordinates of the vertices of triangle ABC are A(4, 1), B(-3, 2) and C(0, k). Given that the area of triangle ABC is 12 sq. unit. Find the value of k.
4. Find the co-ordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
5. If A(6, -1), B(1, 3) and C(k, 8) are three points such that AB = BC. Find the value of k.
6. Find the area of the quadrilateral whose vertices taken in order are A(-5, -3), B(-4, -6), C(2, -1) and D(1, 2)
7. For what value of ‘k’ the points A(1, 5), B(k, 1) and C(4, 11) are collinear?
8. In what ratio does the point P(2, -5) divide the line segment joining A(-3, 5) and B(4, -9)?
9. Find the ratio in which the line segment joining the points A(3, -6) and B(5, 3) is divided by x-axis. Also find the coordinates of the point of intersection.
10. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find the value of x and y.

Frustum of cone

1.         If the radii of the ends of a bucket 24 cm high are 5 cm and 15 cm. Find the curved surface area of the bucket.

2.         The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Find the volume of  the bucket and also find the surface area of the closed bucket.

3.         A bucket is 32 cm in diameter at the top and 20 cm diameter at the bottom. Find the capacity of the bucket if it is 21 cm deep.

4.         A bucket made up of tin sheet of height 20 cm has its upper and lower ends of radius 24 cm and 8 cm respectively.   Find the cost of bucket full of milk at the rate of Rs 21 per litre and the cost of the tin sheet used if the cost of tin sheet is Rs 7 per 100 sq. cm.

5.         If the radii of the ends of a bucket 45 cm high are 28 cm and 7 cm, determine its capacity and the surface area.

6.         The height of the water bucket is 30 cm and circular ends of it are radius 21 cm and 7 cm respectively. Determine :

(i)                  the capacity of the bucket

(ii)                the curved surface area of the bucket

(iii)               surface area of the bucket when its top is open

(iv)              Surface area of the bucket when its top is closed.

7.         The height of a cone is 20 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/64  of the given cone, at what height above the base is the section made?

8.         A cone of base radius 14 cm and height 30 cm is divided into two parts by a plane parallel to the base and at distance 15 cm from the base. Calculate the ratios of the volumes of two parts.

9.         A piece of metal is in the form of a right circular cone of height 24 cm is to be cut into solids by a plane parallel to the base. Find the height of the conical part if its curved surface is 1/8 of the other part.

10.        The height of a cone is 36 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 8/27 of the volume of the given cone, at what height above the base is section made?

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