Volume (Prism, Pyramid)：練習問題

A triangular prism has a base area of \( 25 \text{ cm}^2 \) and a height of \( 8 \text{ cm} \). What is the volume of the prism?

A square pyramid has a volume of \( 80 \text{ cm}^3 \) and a height of \( 15 \text{ cm} \). What is the side length of its square base?

A rectangular container has a base area of \( 400 \text{ cm}^2 \) and contains water at a depth of \( 12 \text{ cm} \). A solid stone with a volume of \( 2.4 \text{ L} \) is dropped into the container and fully submerged. What is the new depth of the water in cm?

A water bottle has a capacity of \( 1.5 \text{ L} \). What is its volume in cubic centimetres \( (\text{cm}^3) \)?
(Note: \( 1 \text{ L} = 1000 \text{ cm}^3 \))

A right-angled triangular prism has a base with legs measuring \( 5 \text{ cm} \) and \( 4 \text{ cm} \). If the height of the prism is \( 10 \text{ cm} \), calculate its total volume.

Find the volume of a rectangular prism that is 6 cm long, 4 cm wide, and 2 cm high.

A rectangular prism has a volume of \( 150 \text{ cm}^3 \). If its base area is \( 25 \text{ cm}^2 \), what is the height of the prism?

A solid metal rectangular prism has a length of \(15 \text{ cm}\), a width of \(10 \text{ cm}\), and a height of \(8 \text{ cm}\). This prism is melted down and completely recast into 3 identical solid square pyramids. If each pyramid has a height of \(12 \text{ cm}\), what is the side length of the square base of each pyramid?

A local gift shop sells two types of candle containers. Container A is a rectangular prism with a base area of \( 45 \text{ cm}^2 \) and a height of \( 12 \text{ cm} \). Container B is a rectangular pyramid with the same base area and the same height as Container A.

(a) Find the volume of Container A in \( \text{cm}^3 \).
(b) Find the volume of Container B in \( \text{cm}^3 \).
(c) If a customer fills Container A with sand and then pours it into empty Container B boxes, how many Container B boxes can be filled completely?

A rectangular aquarium has a length of \( 30 \text{ cm} \) and a width of \( 20 \text{ cm} \). It is filled with water to a depth of \( 15 \text{ cm} \). A solid metal rectangular pyramid with a base measuring \( 10 \text{ cm} \) by \( 12 \text{ cm} \) and a height of \( 15 \text{ cm} \) is placed into the aquarium and is completely submerged.

(a) What is the volume of the metal pyramid?
(b) Find the rise in the water level of the aquarium after the pyramid is submerged.
(c) What is the final height of the water in the aquarium?