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Math Homework Help

Two Similar Cylinders

published on March 5th, 2008 . by Vanaja


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?

similar-cylinders.JPG

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 Vl= pi r2h

Volume of the smaller cylinder Vs=pi(r/2)2(h/2) =(pir2h )/8 = Vl/8

i.e Vs =Vl /8

Therefore 8 smaller pans can fill one larger pan.

Black & White

published on February 27th, 2008 . by Vanaja

The following figures represent a relationship between two variables.

linear.JPG

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

 

Ans:

y=2x+3

A Sales Chart

published on February 17th, 2008 . by Vanaja

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

Items Price
Cabbage $1.8 for 2
Carrot $0.6 for 1.k.g
Onion $1.75 for 1 carton
Potato $2.05 for 1 carton
Tomato $1 for 1 k.


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 cricket problem

published on September 9th, 2007 . by Vanaja

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

Net Problem

published on August 29th, 2007 . by Vanaja

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?


A football problem

published on August 21st, 2007 . by Vanaja

At a football championship 600 tickets were sold .
Child ticket cost $2 each and adult ticket cost $5 each. The total money collected for the game was $1650.

Find the number of tickets sold in each category.
Hint:
Let x be number of children and y be number of adults.
x+y = 600
2x+5y= 1650
==>x= 450, y=150

Ana-The bearer

published on May 30th, 2007 . by Vanaja

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%

Triangle Problem

published on May 5th, 2007 . by Vanaja

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

Area Problem

published on April 18th, 2007 . by Vanaja

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

Temparature Problem

published on April 17th, 2007 . by Vanaja

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

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