Math Homework Help

The two cylindrical pans are similar. The diameter of the smaller pan is equal to the radius of the larger pan. How many of these smaller cans could fill the larger can?

Hint: Since the two cylinders are similar, their dimensions are in the same ratio. It is given that the diameter of the smaller pan is same as the radius of the larger pan. That is the radius of the two pans are in the ratio 2:1. In other words we can say if the radius of the larger pan is ‘r’ the radius of the smaller pan is r/2 and since they are similar their heights are also in the same ratio 2:1. So, if h is the height of the larger triangle, h/2 is the height of the smaller triangle.

Now,

Volume of the larger cylinder V_l= pi r²h

Volume of the smaller cylinder V_s=pi(r/2)²(h/2) =(pir²h )/8 = V_l/8

i.e V_s =V_l /8

Therefore 8 smaller pans can fill one larger pan.

The following figures represent a relationship between two variables.

Which rule relates x the number of dark squares to y, the number of white squares?

Ans:

y=2x+3

Sarah went to a grocery shop. There was a sales chart.

Sarah bought 4 carton potatoes and 1 cabbage. If she gave $10, how much money she got back?

Hint: 10-{(4×2.05)+.9}

A group consists of 50 students. Out of these 20 are girls .There are 10 Australian students. Out of 50 students, 25 students like cricket.
What is the probability of selecting an Australian girl who likes cricket?

Hint:

Probability of selecting a girl= 20/50
Probability of selecting an Australian student = 10/50
Probability of a student like cricket=25/50

Therefore the the probability of selecting an Australian girl who likes cricket= (20/50 )(10/50)(25/50) = 1/25 =0.25

The following is the net representation of a cube.

How will you place the letters L, A, F on the figure so that it should spell LEAF around the sides of the cube?

Today we have a questions on percentage.

Ana is working in a restaurant as a bearer.

As a penalty Ana’s wages were decreased by 50%.
After one month the reduced wages were increased by 50%.

Find her loss.

Hint: The salary increased is the 50% of the decreased salary.

Answer:

New salary is 50+25=75
Therefore loss=25%

Today we have a problem on triangle

Hint:

Since AB=BC, angle C= angle A (Angles opposite to equal sides are equal)

Also, Sum of the angles is 180 º

Answer

55 º

John has a rectangular lawn of dimensions 50 meter by 40 meter.

It has two roads each 2 meter wide running in the middle of it one parallel to the length and one parallel to the breadth. He wants to tar the road.

Find area of the roads to be tarred.

Hint:

We have two roads to be tarred. One is horizontal and the other is vertical.

So, area to be tarred is the area of the two roads which are rectangular in shape.

Area of a rectangle is length x breadth.

Area of the horizontal road = 2 x 50=100 sq.m

Area of the vertical road = 2 x 40=80 sq.m

So,the total are of the two roads=100+80=180 sq.m

But, the roads are crossing at the middle. It is a square portion of sides 2m by 2m in dimensions and we can see that two times we added that area. So, we should subtract that area from the total area of the two rectangular roads.

Area of the square portion is 2 x 2=4 sq.m

Therefore, the area to be tarred = Total area of the two rectangles - The common area

Ans: 176 sq.m

The average temperature of for Monday, Tuesday and Wednesday was 30ºC.
The average temperature for Tuesday, Wednesday and Thursday was 29º C. The Temperature on Thursday was 32º C.

What was the temperature on Monday?

Hint:

Total temperature on Mon,Tue and Wed = 30ºC*3 = 90ºC
Total temperature on Tue,Wed and Thu = 29ºC*3 = 87ºC

Total temperature on Tue and Wed = Total temperature on Tue, Wed and Thu -Temperature on Thu = 87ºC-32ºC= 55ºC

Now, Temperature on Monday can be calculated as follows

Temperature on Monday = Total temperature on Mon,Tue and Wed-Total temperature on Tue and Wed

Ans: 35ºC