A cylinder is surmounted by cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of cylinder is 6.5 cm, and the total height of structure is 12.8 cm. Find the volume of the structure.

The scatterplot above shows the revenue, in millions of dollars, that a company carned over several years and a line of best fit for the data. In Year 4 , the difference between the actual revenue and the predicted revenue is  n million dollars, where  is a posative integer. What is the value of  n ? Round your answer to the nearest whole number. (Disregard the 5 sign when gridding your answer.)

Note:
As we are not certain if the point of the actual revenue is exactly at the midpoint of 50 and 60, so instead of taking the midpoint 55, we can also take it to be 54 or 56.
Then the value of n can be 4 or 6 too.

Sheela wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500m² and the perpendicular distance between the two parallel sides is 100m , find the length of the side along the river.

Which of the following lines pass through origin?

The perimeter of a rectangle is 28 cm and its length is 8 cm. Find its:
(i) breadth (ii) area

Find the area of a trapezium whose parallel sides are 77cm and 60cm and the other two sides are 25cm and 26cm.

Find the total area in the given figure.

A cylindrical jar whose base has a radius 15 cm. is filled with water up to a height of 20 cm. A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water. Find the increase in the level of water?

The parallel sides of a trapezium are 30cm and 40cm and the other sides are 24cm and 26cm. Find its area?

A right triangular park is to be designed such that the angles other than 90° must be equal. What should be the angle dimensions of the park?

A regular polygon with 3 sides is shown below. Find the value of x.

5 If , also find the value of .

What additional information is necessary to prove that the given triangles are congruent by AAS congruence postulate?

Are the given triangles congruent? Explain why or why not.

Are the given triangles congruent? Explain why or why not.

Prove that triangles ACB and ACD are congruent.