Level 3 PSLE
A rectangular block A was cut along the dotted line into two smaller rectangular blocks of equal height, B and C, as shown. The volume of C is 1400 cm³ more than that of B.

1. What is the height of each block?
2. Pete packed 6 of block C such that they fit exactly into a box with a square base. The box has the same height as C. At most, how many of block B can be packed into such a box?

Level 3
The diagram shows a container made of some identical sections. Figure A shows one section of the container. When 5828 cm³ of water was poured into the container, find the water level in the container.

Level 3 PSLE
David has 8 large cubes and some small cubes. He placed them in a rectangular tank. The tank was filled to the brim exactly. The diagram shows the first layer of cubes.

1. How many small cubes does David have?
2. The volume of the tank is 504 cm³. If the large cubes took up ³₇ of the tank, What is the length of the edge of one small cube?

Level 3
In the diagram not drawn to scale, Tank J and Tank K each has a button that, when pressed, will cause the water to flow out if the water level is higher than the hole. Tank J measures 134 cm by 42 cm by 137 cm. Tank K measures 55 cm by 21 cm by 68 cm. Tank L is 69 cm by 20 cm by 26 cm. Both holes are located at a height of 14 cm from the top of their respective containers. When Tank J is completely filled with water and both buttons are pressed, what will be the final water level in Tank L?

Level 3 PSLE
A and B are two rectangular containers. The base area of A is 30 cm² and the base of B has dimensions as shown. A contained 750 cm³ of water and B was empty.

1. What was the height of the water level in A?
2. Ben poured some water from A into B without spilling. After that, the height of the water level of A was the same as that of B. How much water did Ben pour into B?

Level 3
Tank A measuring 40 cm by 17 cm by 146 cm is filled with water. Tank B is with a square base of side 68 cm is empty. Water is poured from Tank A into Tank B until the water level in Tank B is twice the height of the water in Tank A. What is the height of the water level in Tank B?

Level 3
This figure is not drawn to scale. A rectangular glass tank 72 cm by 50 cm by 35 cm has 2 compartments, X and Y, with a water height of 30 cm in X and 15 cm in Y. A hole in the slider caused water to leak from X to Y. It was found that the water level in both compartments became the same after some time.

1. What is the height of water in the tank now?
2. It took 1¹₂ h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from X to Y in 1 minute? Express the answer to 1 decimal place in cm³.

Level 3 PSLE
Ray had a rectangular block of wood 12 cm by 8 cm by 6 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Ray then cut the block into 1-cm cubes. How many of these cubes have none of the faces painted?
3. How many of these cubes have 2 of the faces painted?

Level 3
The figure shows a wooden cuboid that measures 125 cm by 20 cm by 20 cm.

1. Find the maximum number of 3-cm cubes that can be cut from the wooden cuboid.
2. Find the total surface area of the L-shaped block after cutting.

Level 3 PSLE
An open rectangular box is shown.

1. The inside of the box including the base is painted. Find the painted area.
2. When the box is packed full with 1-cm cubes, how many cubes are there?
3. How many cubes touch inside the box as a result?

Level 3 PSLE
The figure shows the amount of water in two rectangular Tanks, A and B, at first.
Ray poured ¹₄ of the water from A into B to fill it to the top, without overflowing.

1. How much water was there in A at first?
2. Ray then poured all the water from B into A. 720 cm³ of water overflowed from A. What was the height of A?

Level 3
The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 40 cm by 25 cm by 25 cm and 2 similar cubes of sides 5 cm. Line A is 10 cm. 12.5 ℓ of water is poured into the top cube into the cuboid.

1. What is the height of the water level from the base of the container?
2. How much more water in cm³ must be poured in so that the water fills up half of the top cube?

Level 3
The figure, not drawn to scale, shows an empty tank measuring 20 cm by 15 cm by 15 cm. Water flows from Tap A at a rate of 300 mℓ per minute and from Tap B at a rate of 180 mℓ per minute. Tower X and Tower Y have a base area of 20 cm² and 30 cm² respectively. Water is drained out of the container at a rate of 130 mℓ per minute. Find the height of the water level after 13 minutes.

Level 3 PSLE
The figure shows taps A and B and an empty tank. At 2 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 3.8 litres per minute. After 5 minutes, tap B was turned on. At 2.15 p.m., the tank was half filled with water.

1. How many litres of water flowed out of tap B in 1 minute?
2. At 2.30 p.m., what fraction of the tank was filled with water?

Level 3
Water flows into a tank through Tap A and flows out of the container through Tap B. The capacity of a tank is 40 litres. When only Tap A is turned on, the container is completely filled in 16 minutes. When only Tap B is turned on, it takes ¹₃ hour for all the water to flow out. If both taps are turned on at the same time,

1. How long does it take to fill 40% of the tank?
2. How much water has flowed out through Tap B by the time the tank is ³₅ filled with water?