1) A box has a mass of 29 kg when it is 5⁄6 filled with sand.
When it is 1⁄5 filled with sand, it has a mass of 10 kg. Find the mass of the empty box.
Ans :- The mass of the empty box is 25 kg.
2) Container A and B are containers with the same square base. Container A contains water filled to the brim while Container B is empty. After 288 cm³ of water is poured into Container B from Container A, the depth of water in Container B is 60% the depth of water in Container A. What is the length of the square base of Container B?
Ans :- The length is 4 cm.
3) A rectangular tank, 80 cm long. 50 cm wide and 40 cm tall is ¼ filled with water. All the water in the tank is poured into pails of capacity 0.5 litres each. Find the minimum number of such pails needed.
Ans :- Minimum 80 such pail needed .
4) A metal container when 0.6 full of nails had a mass of 48 kg. John found that he needed another 30 kg of nails to fill up the container. What was the mass of the container when it was full of nails?
Ans :- 78 kg.
5) The figure below shows a solid made up of 14 identical cubes. When the whole solid is painted blue, the total area being painted is 672 cm². What is the volume of this solid?
Ans :- 896 cm³.
6) Zachary glued cubes of side 3 cm together and made a model as shown below.
(a) What was the volume of the model?
(b) Zachary then took the whole model to his brother to paint it red, including the base. Find the total area of the faces painted red.
Ans :- a) Volume of the model is 270 cm ³
b) The total area of the faces painted red is 324 cm²
7) At a funfair, Sharifah made some fruit punch by mixing 5 bottles of syrup with water. Each bottle contained 3 litres of syrup and she added 3 litres of water to every litre of syrup. Then she sold all the fruit punch in cups of 300 ml each. If a total amount of $180 was collected from the sales, how much did each cup of the fruit punch cost?
Ans :- Each cup of fruit punch cost $0.90
8) The mass of Ashley is 15 kg more than that of Betty and 12 kg more than that of Charlie. Their average mass is 68 kg. What is the average mass of Ashley and Charlie?
Ans :- Average mass is 71 kg.
9) A 25 cm square based steel tank has a height of 30 cm. It is 5⁄6 filled with water. Some of the water from the steel tank is poured into a recangular glass container measuring 40 cm by 15 cm by 18 cm until it is completely full. How many litres of water are left in the steel tank?
Ans :- 4.825 ℓ water left in the tank.
10) The mass of a bag of sugar is 3⁄8 kg. The mass of a bag of flour
is 4⁄9 of the mass of the bag of sugar. If the mass of a packet of peanuts is 3⁄8 of the mass of the bag of flour, what is the mass of the packet of peanuts? Leave your answer in grams.
Ans :- 100g.