Ratios and volumes questions

Question

1.       Work out these ratios in simple whole numbers

a)      35% wool, 65% rayon

b)      ¾ cup butter, 1 ¾ cups flour

c)       2.5 cups milk, 4.5 cups flour

d)      150ml cordial to 1 liter water

 

2.  a) Dry cement mix used for making concrete is made by mixing sand, cement and gravel in the ratio 1:3:4. To make a total volume of 120 shovels of dry mix, how much of each ingredient should be used?

b) If you got $37.50 for 5hours work, how much do you get for 17 hours work?

3.

a) We have a map scale 1:32000. How many kilometres is represented by 1cm on the map?

b) Change the scale 1.5cm to 450meters into a ratio.

4.

a) The drug erythromycin comes in ampoules of 100mg per 2ml.

(i) An adult patient requires 150mg. What volume of the drug is needed?

(ii) A child’s dosage is 5mg per kg weight. Sarah weighs 22kg. How many millilitres of dosage will she require?

b) The drug tetracycline comes in 250mg and 150mg tablets. A patient requires 550mg of tetracycline. How many whole tablets of each strength will be needed?

5. 250ml cleaner is made up to a 4 liter solution.

a) What volume of water was added?

b) What is the percent concentration of the solution

6.

a) What is the gear ratio of theses gears?

b) The large gear rotates at 60rpm. What is the speed of the small gear?

7.  What is the mechanical advantage of the following situations?

a) A 1.8 meter crowbar opening a crate. The distance to the edge of the crate is 1.6m

b) A gangplank of 14 meters rises 1.2 meters.

8. Gerry uses a 3 meter plank to roll barrels up to a shelf 1.5 meters above the ground.

a) What is the mechanical advantage of using the plank?

b) What fraction od effort does he make?

c) He applies 10 newton of force. What force is applied to shift the barrels?

Answer 1

2)a) sand, cement and gravel in the ratio 1:3:4.

To make a total volume of 120 shovels of dry mix

x+3x+4x = 120

8x = 120

x = 120/8

x = 15

Sand = 15

Cement = 15*3 = 45

Gravel = 4*15 = 60

To make a total volume of 120 shovels of dry mix we should use 15 shovels sand,45 shovels cement and 60 shovels gravel.

b) For 5 hours work got $37.50

For 1 hour simply we got 37.50/5 =$ 7.5

For 17 hours work we got = 7.5*17 =$ 127.5

 

 

Answer 2

4)a)(i)  erythromycin drug 100mg per 2ml

For 1 mg = 2/100ml

An adult patient requires 150mg

2/100*150

An adult patient requires  3ml.

(ii) A child’s dosage is 5mg per kg weight

Sarah weighs 22kg = 22*5 = 110 mg

Sarah requires 2/100*110 = 2.2ml

Answer 3

(1).

(a). Ratio = 35% wool : 65% rayon

                = 35/100 : 65/100

                = 35 : 65

                = 7 : 13.

 

(b). Ratio = ¾ cup butter : 1 ¾ cups flour

                = 3/4 : 7/4

                = 3 : 7.

 

(c). Ratio = 2.5 cups milk : 4.5 cups flour

                = 2.5 : 4.5

                = 25/10 : 45/10

                = 25 : 45

                = 5 : 9.

 

(d). Ratio = 150 ml cordial to 1 liter water

                = 150 ml : 1000 ml

                = 3 : 20.

Answer 4

(3).

(a). Ratio of map scale = 1 : 32000 that means 1 unit equals to 32000 another units.

Therefore 1 cm = 32000 kilometers on the map.

(b). Ratio = 1.5cm : 450

                = 15/10 : 450

                = 15 : 4500

                = 1 : 300

Therefore, 1 cm = 300 meters.

Answer 5

(5).

Ratio = 250 ml cleaner : 4 liter solution.

(a).

Solution = water + cleaner

⇒ 4L = water + 250 ml

⇒ water = 4L - 250 ml

⇒ water = 4000 ml - 250 ml

⇒ water = 3750 ml

⇒ water = 3.75 L.

The volume of water is 3.75 L.

 

(b).

Here both solute(cleaner) and solvent(water) are liquids, so the concentration may be expressed as percent by volume.

Percent by volume = (volume of solute / volume of solution) * 100 %.

                              = (250 ml / 4 L) * 100 %

                              = (250 ml / 4000 ml) * 100 %

                              = 6.25 %.

The concentration of the solution is 6.25 %.

Answer 6

(6).

This equation shows that if the number of teeth on the output gear G_B is larger than the number of teeth on the input gear G_A, then the input gear G_A must rotate faster than the output gear G_B.

Answer 7

(7).

The distance mechanical advantage also is : MA_D = d_L/d_E, where

d_L is the distance of the load to the fulcrum.

d_E is the distance of the effort to the fulcrum.

(a). MA_D = d_L/d_{E =} 1.8/1.6 = 9/8 = 1.125.

 

(b). MA_D = d_L/d_{E =} 14/1.2 = 9/8 = 11.667.
 

Answer 8

(8).(a).

Mechanical Advantage =  Length of inclined plane / height of inclined plane = 3m / 1.5m = 2.