Volume (Water displacement method, Irregular solids)：練習問題

A measuring cylinder contains \(255 \text{ mL}\) of water. After a piece of coral is placed into the cylinder and fully submerged, the water level rises to \(312 \text{ mL}\). What is the volume of the coral?

A rectangular tank has a base area of \(120 \text{ cm}^2\) and a total height of \(25 \text{ cm}\). It is initially filled with water to a depth of \(22 \text{ cm}\). When an irregular metal block is fully submerged in the tank, \(450 \text{ mL}\) of water overflows. What is the volume of the metal block?

A rectangular container with a base area of \(240 \text{ cm}^2\) is partially filled with water. An irregular solid is submerged, causing the water level to rise by \(2.5 \text{ cm}\). If the solid is then cut exactly in half and only one half is submerged in the same container, what would be the rise in water level?

When an irregular solid is completely submerged in a container of water, the volume of the water displaced is equal to the ____________ of the solid.

A measuring cylinder has a maximum capacity of \(300 \text{ mL}\). It initially contains \(220 \text{ mL}\) of water. When an irregular metal block is fully submerged, the water level rises to \(290 \text{ mL}\). If a second identical metal block is then fully submerged in the same cylinder, how much water will overflow?

Two identical metal bolts are dropped into a measuring cylinder, causing the water level to rise from \(160 \text{ mL}\) to \(196 \text{ mL}\). Calculate the volume of one metal bolt.

A rectangular tank with a base area of \(240 \text{ cm}^2\) is initially filled with water to a depth of \(10 \text{ cm}\). When an irregular stone is fully submerged in the tank, the water level rises to \(13.5 \text{ cm}\). Find the volume of the stone in \( \text{cm}^3\).

A rectangular tank, Tank A, has a base area of \(400 \text{ cm}^2\) and a total height of \(50 \text{ cm}\). It is initially filled with water to a depth of \(35 \text{ cm}\). When an irregular metal block, Object P, is fully submerged in Tank A, the water level reaches the brim and exactly \(1800 \text{ cm}^3\) of water overflows into an empty rectangular container, Container Q. Container Q has a base area of \(150 \text{ cm}^2\) and a total height of \(20 \text{ cm}\). If a second irregular stone, Object S, is then fully submerged into Container Q while it still contains the water from the first overflow, the water level in Container Q reaches the brim and \(250 \text{ cm}^3\) of water overflows. Find the volume of Object S in cubic centimetres (\(\text{cm}^3\)).

A measuring cylinder is partially filled with water up to the \(300 \text{ mL}\) mark.
a) When an irregular stone is placed into the cylinder and completely submerged, the water level rises to \(375 \text{ mL}\). What is the volume of the stone in \(\text{cm}^3\)?
b) Later, a small metal toy is also dropped into the cylinder and completely submerged alongside the stone. The water level rises further to \(410 \text{ mL}\). What is the volume of the metal toy in \(\text{cm}^3\)?
c) If the measuring cylinder has a total capacity of \(500 \text{ mL}\), how many more cubic centimetres (\(\text{cm}^3\)) of water would be needed to fill the cylinder completely to the top?

A rectangular tank has a base area of \(450 \text{ cm}^2\) and a total height of \(30 \text{ cm}\). It is initially filled with water to \(\frac{2}{5}\) of its height.

(a) An irregular solid object (Object X) is fully submerged into the tank, causing the water level to rise to \(24 \text{ cm}\). Find the volume of Object X in \(\text{cm}^3\).

(b) After Object X is removed, another irregular stone (Object Y) is fully submerged in the tank. This causes the water level to reach the brim, and exactly \(900 \text{ mL}\) of water overflows into a collecting basin. Calculate the volume of Object Y.

(c) If both Object X and Object Y were placed into the tank together when it was at its initial water level, how many millilitres (mL) of water would overflow?