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Eexercise - 27 The total surface area of a closed right circular cylinder is 65/2cm 2 and the circumference of its base is 88cm. Find the volume of the cylinder. The volume of a vessel in the form of a right circular cylinder is and its height is 7cm. Find the radius of its base. The height of a cylinder is 15cm and its curved surface area is 660 sq.cm. Find its radius. A cylindrical tank has a capacity of 6160 cu.cm. Find its depth if the diameter of its base is 28m. Also, Find the area of the inside curved surface of the tank. The volume of a right circular cylinder is 1100 cu.cm and the radius of its base is 5cm. Find its curved surface area. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder. 50 circular plates, each of radius 7cm and thickness 0.5cm are placed one above the other to form a solid right circular cylinder. Find the total surface area and volu...

Combination of Solids In our day-today life wer come across different solids which are combination of two or more solids. For example, top is a combination of a hemisphere and cone, circus tent is a combination of cone and cylinder. In this section we shall deal with such types of solid and find their surface area and volume. Example 6. A solid toy is in the form of a hemisphere surmounted by a right circular cone. If height of the cone is 4cm and diameter of the base is 6cm, Calculate: The volume of the toy The surface area of the toy. Solution:- Radius, r of cone = 6/2 = 3cm Height, h of cone = 4cm Radius, r of hemisphere = 3cm Slant height (i) Volume of the toy = volume of cone + volume of hemisphere (ii) Surface area of the toy = Curve surface area of cone + curved surface area of hemisphere = 3.14 X 3 X (5 + 2 X 3) = 103.62cm 2   Example 7. A circus tent is cylindrical to a height of 3m and conical above it. If its base radius is 52.5m and slant height of the conical portion is ...

  Exercise - 32 A(3, 2) and B(-2, 1) are two vertices of a triangle ABC, whose centroid has coordinates (5/3, -1/3). Find the coordinates of the third vertex C of the triangle. Show that the points A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle. Determine the ratio in which the points (6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a. Find the point on the x-axis which is equidistant from the points (-2, 5) and (2, -3). The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q. Two vertices of a triangle are (1, 2) and (3, 5). If the centroid of the triangle is at the origin, find the coordinates of the third vertex. If ‘a’ is the length of one of the sides of an equilateral triangle ABC, base BC lies on x-axis and vertex B is at the origin, find the coordinates of the vertices of the triangle ABC. The coordinates of the mid-point of the line joining the points (2p+...

Sometimes we say, “probably it may rain” or “Probably he may get more than 90% in the examination" etc. These are elements of certainty. Means we are not certain about some things. In mathematics these comes under Probability. The theory of probability is widely used in the area of natural as well as social science. Probability as a Measure of Uncertainty Suppose we through a die which is a well balanced cube with its six faces marked numbers from 1 to 6, one number of one face, we see the number which come up on its uppermost face. A die can fall with any of its face upper most. The number on each of the face is equally libely and possible outcome. There are six equally likely ealy outcomes: 1, 2, 3, 4, 5 or 6 in a single throw of a die. The chance of any number ‘say 3’ to come up is 1 out of 6. That is probability of 3 coming up is 1/6 i.e. p(3) = 1/6 Similarly in tossing a coin, we may get either head (H) or tail (T) up and P(H) = ½ Hence probability of an event E is There are...