Question

AREA, PERIMETER & VOLUME, USE, CONVERT & CALCULATE QUESTIONS:

---------------------------------
QUESTION 1:
The arena’s car park is shown below.
( SEE DIAGRAM)
Area of a circle = πr2
π = 3.14

What is the area of the car park, not including the arena itself in m2?

-------------------------------

QUESTION 2:

The arena management want to put a perimeter fence around the car park.

( SEE DIAGRAM) ( SAME AS BEFORE)
How many metres of fencing would be needed, not including the arena and a 5 metre space for a gate?

----------------------------------
QUESTION 3:

Around the car park, cylindrical concrete bollards are going to be placed.

Volume of a cylinder:

V = area of the base x height
V = πr2h
π = 3.14

( SEE DIAGRAM)

Find out how much concrete each one will need by working out its volume in cm3 from the diagram.

------------------------------
QUESTION 4:
You are working as an office apprentice for the bksb Newcastle Arena.

The current exchange rate for US dollars ($) to British pounds (£) is this:

$1.54 : £1

The American folk band, Patriots & Banjos, only accepts payment for concerts in US dollars. The agreed fee was £12,000.

How many dollars will the arena have to pay them?

-----------------------------
QUESTION 5:
To prepare the arena for a concert takes 62 3/4 hours of work.
How many minutes is this?


The arena set-up team’s work schedule is shown in the table below. Convert the minutes worked into hours.
Staff Member Minutes Worked Hours Worked?
Mike Chewer 870 ?
Jennifer Glass 225 ?
Fred Carlton 75 ?
Amy Amaretto 720 ?

-----------------------------
QUESTION 6
The exchange rate is £1 = $1.76. If he earns £135, how many Australian dollars will he get?

The arena’s stage is 8 metres long. The left hand and right hand sides of the stage will be taken up by large speakers with a 130 cm base each.
How many metres of the stage will be left free for the band?
-----------------------------
QUESTION 7:

The band has a banner at the back of the stage. It is 631 centimetre long.
Approximately how many metres is this?
(Answer to 1 decimal point)


For health and safety reasons, the temperature of the arena must be strictly controlled.
If the temperature is 36 ºC what is it in ºF

Use this formula to help you:

F = C x 9/5+ 32 = ?

--------------------------------

QUESTION 8:

You are helping move equipment. It is company policy at the arena that, without assistance, no one should lift more than 30 kg.

One item weighs 0.76 kg, and there are 40 items in one box.

Do you think are you allowed to lift the box up on your own?
Yes OR NO?
---------------------------
QUESTION 9:

Look at the conversion table below.
KG LBS
1 2.2
2 4.4
3 6.6
4 8.8
5 11.0
6 13.2
7 15.4
8 17.6
9 19.8

You are asked to lift something that is 15 kg. How many pounds is it?
You pick up something that weighs 48.4 lbs. How many kilograms is this?
--------------------------
QUESTION 10:
To get to the arena from the airport, the band has to travel 59 kilometres. If they travel 40 kilometres per hour, how long does it take them to arrive at the airport?

Select the correct answer.

1 hr 47 mins
1.475 mins
88 mins
68 mins

THANKYOU SO MUCH FOR YOUR HELP IN ADVANCE

Answer 1

1.
`6518.75 m^2`

2. 295 m of fencing is needed

3.
`V=653,120cm^(3)`

4. $18,480

5. Part 1:
`62(3)/(4)Hours=3,765Minutes`

AND Part 2:

Mike Chewer 870 mins = 14.5 hours

Jennifer Glass 225 mins = 3.75 hours

Fred Carlton 75 mins = 1.25 hours

Amy Amaretto 720 mins = 12 hours

6. Part 1: $237.6; AND Part 2: 540 cm (or 5.4m)

7. Part 1: 6.3 m; AND Part 2: 96.8ºF

8. No.

9. Part 1: 15 kg = 33 pounds AND Part 2: 48.4 pounds = 22 kgs

10. 1.475 hours

Explanation:

1. Area of car park is area of rectangle (length * width) - area of half circle of arena (half circle area is
`(\pi r^2)/(2)`

Length is given as 100 and width is 75, also the radius of the circle is half of 50, which is 25. Putting all of these we get:

Area of car park =
`(100*75)-((\pi (25)^2)/(2))=6518.75 m^2`

2. Looking at the diagram carefully, we can see that the perimeter (sum of all the sides) would be sum of top side (100 m), right side (75 m ), bottom side (100 m) and left side that is left ( area covers 50m and gate of 5 m, so covers 55m, left is 75 - 55 = 20)

Perimeter is
`100+75+100+20=295`. So 295 m of fencing is needed

3. Volume of cylinder is
`V=\pi r^2 h`

We need in cm, so we need to convert 1.3m to centimeters. Since there are 100 cm in 1 m, 1.3m is equal to 130 cm. Also, radius is half of 80cm, which is 40 cm. Putting these into the formula we get:

`V=\pi r^2 h\\V=(3.14)(40)^2(130)\\V=653,120cm^(3)`

4. If $1.54 : £1 , then £12,000 would be 12,000 multiplied by 1.54. So:

`12,000*1.54=18,480` dollars

5. Part 1: To convert to minutes, we multiply
`62(3)/(4)` by 60. Thus we have
`62(3)/(4)*60=3,765` minutes

Part 2: Mike Chewer worked 870 minutes, to convert to hours, we divide by 60. So
`(870)/(60)=14.5` hrs

Jennifer Glass worked 225 minutes, to convert to hours, we divide by 60. So
`(225)/(60)=3.75` hrs

Fred Carlton worked 75 minutes, to convert to hours, we divide by 60. So
`(75)/(60)=1.25` hrs

Amy Amaretto worked 720 minutes, to convert to hours, we divide by 60. So
`(720)/(60)=12` hrs

6. Part 1: If £1 = $1.76, to get australian dollars for £135, we multiply 135 by 1.76. So we have
`135*1.76=237.6`

So that's $237.6

Part 2: Converting 8 m to cm, we multiply 8 by 100, so it is 8*100=800cm. Since both sides will be taken by 130 cm speakers, so a total space of 2*130=260cm will be taken. So amount of space left for the band, in cm, is 800 - 260 = 540 cm (or 5.4m)

7. Part 1: To convert cm to meters, we divide it by 100. So we have:

`(631)/(100)=6.31`

Rounding to 1 decimal place, it is 6.3m

Part 2: The formula to convert Celsius to Fahrenheight is
`F=1.8C+32`

Plugging C=36 into this, we get F:
`F=1.8C+32\\F=1.8(36)+32\\F=96.8`degrees

8. One item weights 0.76 kg so 40 items (in 1 box) would weigh
`40*0.76=30.4`kg

According to policy, it is over 30, so you won't be allowed to lift it. So, NO!

9. We can see that 1 kg is 2.2 lbs (conversion factor). So 15 kg is 15 * 2.2 = 33 pounds.

Also, To get pounds into kgs, we divide the pounds by 2.2. So 48.4 lbs is 48.4 divided by 2.2 which is 22 kg.

10. We need to divide 59 km by 40 to get the amount of time it will take (distance divided by rate is time). So
`(59)/(40)=1.475Hours`

Second answer choice is a bit wrong, it should be 1.475 hours. Correct answer is 1.475 hours.