Surface area and volume
1. Water flow at the rate of 10 meters per minute through a cylindrical pipe having the diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth24cm?
2. A well, whose diameter is 7cm, has been dug 22.5m deep and the earth dugout is used to form an embankment around it. If the height of the embankment is 1.5m, find the width of the embankment.
3. A conical vessel whose internal radius is 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises.
4.A solid sphere of radius 3cm is melted and then cast into small balls each of radius 0.3cm. Find the no. of balls thus obtained.
5. Water flow at the rate of 10 meters per minute through a cylindrical pipe having the diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth24cm?
6. The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its volume.
7. A bucket is in the form of a frustum of a cone ad holds 28.490 liters of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.
Co-ordinate Geometry
1. If the points A(x, 2), B (-3,-4) and C (7, -5) are collinear, then what is the value of x?
2. Find the ratio in which the y-axis divides the line segment joining the points (-4,-6) and (10, 12). Also find the coordinates of the point of division.
3. If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.
4. Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1).
5. If the points A(-2,1), B (a, b) and C(4, -1) are collinear and a – b = 1, find the value of a and b.
6. The three vertices of a parallelogram ABCD are A(3, -4), B(-l, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of parallelogram ABCD.
7. Find the value of k, if the point P(2,4) is equidistant from the points A(5, k) and B(k, 7).
1. Water flow at the rate of 10 meters per minute through a cylindrical pipe having the diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth24cm?
2. A well, whose diameter is 7cm, has been dug 22.5m deep and the earth dugout is used to form an embankment around it. If the height of the embankment is 1.5m, find the width of the embankment.
3. A conical vessel whose internal radius is 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises.
4.A solid sphere of radius 3cm is melted and then cast into small balls each of radius 0.3cm. Find the no. of balls thus obtained.
5. Water flow at the rate of 10 meters per minute through a cylindrical pipe having the diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth24cm?
6. The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its volume.
7. A bucket is in the form of a frustum of a cone ad holds 28.490 liters of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.
Co-ordinate Geometry
1. If the points A(x, 2), B (-3,-4) and C (7, -5) are collinear, then what is the value of x?
2. Find the ratio in which the y-axis divides the line segment joining the points (-4,-6) and (10, 12). Also find the coordinates of the point of division.
3. If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.
4. Find the area of the triangle ABC with A (1, - 4) and mid-points of sides through A being (2, - 1) and (0, -1).
5. If the points A(-2,1), B (a, b) and C(4, -1) are collinear and a – b = 1, find the value of a and b.
6. The three vertices of a parallelogram ABCD are A(3, -4), B(-l, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of parallelogram ABCD.
7. Find the value of k, if the point P(2,4) is equidistant from the points A(5, k) and B(k, 7).
