Circumference
Surface Area
Volume
Pi
100
What is the diameter when the circumference is 6.28 cm?
When the circumference is 6.28 cm, the diameter is: Circumference/π=6.28/3.14=2 cm
100
When the radius of a circle is expanded by the factor of x. How does the surface area of this circle change?
The surface area of this circle expanded by the factor of x^2. ----the formula of calculating surface areas of circles is: Pi*r^2 when r expands by the factor of #, the surface area expands by the factor of #^2.
100
What is the volume of a cylinder?
The volume of the cylinder is the measure of the amount of space inside of a cylinder.
100
What is Pi?
Pi is an irrational number. Pi is a quotient of the circumference of its diameter. It is also the 16th Greek letter.
200
When the surface area of a circle is 200.96cm^2, the circumference of the circle is: r=√(200.96/3.14)=√64=8cm C=2*Pi*r=2*3.14*8=50.24cm
What is circumference of the circle when the surface area of a circle is 200.96 cm^2?
200
On the middle of the square, there is a parterre, which has a shape of a circle. the circumference of the parterre is 62.8 m. what is the covering area of the parterre?
the radius of the parterre: C/Pi/2=62.8/3.14/2=10 m the covering area of the parterre: Pi*r^2=3.14*10^2 =3.14*100 =314 m^2
200
There is a bucket, which is a cylinder. The measurements are: r=20 cm, h=30 cm. What is the volume of the bucket?
the volume of a cylinder: Pi*r^2*h =3.14*20^2*30 =3.14*12000 =37680 cm^3
200
When we use Pi in our lives?
We often use it for calculating the circumferences, surface areas, and volumes of circles, cylinders, cones, and so on.
300
There is a clock on the classroom wall. The minute hand is 10 cm. when the time passed an hour, the top of the minute hand went ( ) cm.
the minute hand is the radius of the space it went pass. The top of the minute hand went: Pi*2*r =3.14*2*10 =62.8 cm
300
There is an iron wire in the box. We can use the wire to make a circle which has the surface area of 1256 cm^2. Now, we make it into a square. What is a side of the square?
Formula: Pi*r^2 the diameter of the circle: 1256/3.14=400 m √400=20 m the circumference of the circle: 3.14*20=62.8 m since that C square=Circumference therefore the perimeter of the square is 62.8 m one side of the square is: 62.8/4=13.2 m
300
It is a cylinder glass container. The diameter of the base is 8 cm. The container contains 16 cm deep of solid, which is the 4/5 of the whole container. how much water can this container contain?
the volume of the solid inside the container: Pi*r^2*h =3.14*(8/2)^2*16 =3.14*256 =803.84 cm^3 the volume of the whole container: Solid/its fraction =803.84/(4/5) =1005 cm^3
300
Since Pi is an irrational number, how can we calculate with Pi?
Usually, we use 3.14 instead of the whole number.
400
I have a rectangle color paper. Then, I used this paper to cut out a circle which is the biggest one that I could have. the circumference is 40.82 cm. Please find out the width of this rectangle paper. (Hint: the width is always the shortest side of a rectangle)
The result is to find out the shortest side of a rectangle. It also means that to find out the diameter of this circle. d=C/Pi =40.82/3.14 =13 cm Namely, the width of the rectangle is 13 cm.
400
A farmer sets an automatic sprinkler at the center of the farm. the furthest distance that the sprinkler can spray is 6 meters. what is the maximum surface area that the sprinkler can spray?
the radius: 6 m the surface area that the sprinkler can spray: Pi*r^2=3.14*6^2=113.04 m^2 which is also the surface area of a circle which has the radius of 6 m.
400
A worker puts a cylinder which has the base of 20cm^2 into a container which is a rectangular prism (a=6 cm, b=15 cm, h=7 cm). There is a lot of water in it, but not the full of the container. When he puts the cylinder in it, the water level rises 3 cm. What is the height of the cylinder?
the volume of the rising water: a*b*rising height =6*15*3 =270 cm^3 it is also the volume of the cylinder the height of the cylinder: 270/20 =13.5 cm
400
Write the first 10 decimals of Pi.
3.1415926535
500
A postman has a bike. the diameter of the wheels is 0.8 m, the wheels whirl 100 per minute. Now, he wants to go through a bridge which is 1256 m. how many times does he need?
The circumference of the wheels: 0.8*3.14=2.512 m The bike goes ( ) m per minute: 2.512*100=251.2 m/min To go through the bridge, he needs: 1256/251.2=5 minutes
500
There is a round swimming pool in the garden. The owner wanted to make a path around the swimming pool. The diameter of the swimming pool is 16 m. The width of the path is 2 m. What is the total surface area of the path?
the surface area of the path: Pi*r^2 =3.14*2^2 =3.14*4 =12.56 m^2
500
There is a cylinder wood, which has the height of 2 m. After it is cut into three sections, the surface area increased 12.56 m^2. Find out the original wood's volume.
When the wood is cut into three sections, the surface area is increased because of six extra bases therefore 12.56 m^2 is the sum of six same bases' areas. the surface area of one base is: 12.56/6 =2 m the volume of the wood is: base*h =2*2 =4 m^3
500
How can we get Pi?
Pi is a number which is reckoned from the formula for calculating the circumference of a circle: Pi*d / 2*Pi*r therefore, Pi is the quotient of the circumference and its diameter
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