Solve:  and 

The cross section of a canal is atrapezium in shape. If the canal is 10m wide at the top and 6m wide at the bottom and the area of the cross section is 840 sq. m, find the depth of the canal ?

The total surface area of a cylinder of height 6.5 cm is 220 sq. cm. Find its volume.

In a trapezium, the two non parallel sides are equal in length, each being 5 units. The parallel sides are at a distance of 3 units apart. If the smaller side of the parallel side is of length 2 units, then what is the sum of the diagonals of the trapezium ?

The base radius of a cylinder is 5/3 times its height. The cost of painting its C.S.A. at 2 paise/cm² is Rs 92.40. What volume of the paint is required?

During mineral formation, the same chemical compound can beco me different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees Celsius  , on the horizontal axis, and the pressure p , in gigapascals (GPa), on the vertical axis.

An equation of the boundary line between the andalusite and sillimanite regions is approximated by the equation above. What is the meaning of the T-intercept of this line?

Note;
A phase diagram represents the different physical states of some substance under different conditions, such as termperature and pressure, graphically. It may seem like a complicated graph but we just needed to focus on the equation of one given line.

Solve the system of equation by using elimination: 

Farmer Joe had 35 customers for the whole morning. He knew 20 of them. How many new customers did he meet today ?

Read the problem carefully multiple times in order to understand it.

The budget for a school band was   in 2010 . The budget decreased by  from 2010 to 2011 and then increased by  from 2011 to 2012 . Which of the following expressions represents the budget, in dollars, for the school band in 2012?

Note:
The concept of percentages can be a little tricky. But we just need to remember a few basic things to get going. This is the standard way of finding the value after increasing or decreasing a quantity by a certain percentage

The perimeter of a trapezium is 52cm .Its non parallel sides are equal to 10cm each and its altitude is 8cm. Find the area of the trapezium ?

If the denominator of a certain fraction increased by 1 and the numerator by 2.The fraction becomes equal to 5/8 and if the numerator and denominator are diminished by 1, the fraction becomes equal to 1⁄2. Find the fraction.

Three cylinders each of height 16 cm and radius of base 4 cm are placed on a plane so that each cylinder touches the other two. What is the volume of the region enclosed between the three cylinders?

The parallel sides of an isosceles trapezium are 16cm and 28cm and equal sides are 24cm each. Find the area ?

The sum of the digits of a two-digit number is 7. If the digits are reversed, the number is reduced by 27. Find the number?

Venu has as many sisters as he has brothers. If Karuna, Venu’s sister has thrice as many brothers as she has sisters, then Venu has how many sisters?

A pit 10 m long and 2 m wide is filled with 4.8 cubic m. of sand. What is the depth of the pit?