Volume of Prisms, Cylinders and Pyramids

Sheila believes that the two cylinders shown in the diagram below have equal volumes. Is Sheila correct or incorrect? Select ALL that apply.

• Sheila is incorrect. The volumes of both cylinders are not equal.

• Sheila is incorrect. One of the cylinders is tilted.

• Sheila is correct. When two cylinders have the same base areas and the same height, their volumes must be the same.

• Sheila is correct. Both cylinders radii and height are equal, so their volumes are the same.

• Sheila is correct. Using Cavalieri’s Principle and the formula $v=Bh$ or $v=\pi r^2h$ proves the volumes of the cylinders are equal.

The cross-sectional areas of the right prisms shown are equal. Which of the following is true?

• The volume of the triangular prism is half the volume of the rectangular prism.

• The volume of the triangular prism is twice the volume of the rectangular prism.

• The volume of the triangular prism is equal to the volume of the rectangular prism.

• The volume of the triangular prism is one-third the volume of the rectangular prism.

A certain cylinder has a height of $h_c$ and a certain square prism has a height of $h_p$ . The circular cross section of the cylinder and the square cross section of the prism have the same area. Which equation expresses the relationship of the volume of the cylinder, $V_c$ to the volume of the prism $V_p?$     

•  $V_c=V_p$  

•  $\pi V_c=V_p$  

•  $\frac{V_c}{V_p}=\frac{h_p}{h_c}$  

•  $\frac{V_c}{V_p}=\frac{h_c}{h_p}$  

Kevin is filling the pool in his backyard with water. If the pool is in the shape of a cylinder with a diameter of 12 feet, and a height of 5 feet, how much water is needed to fill  $\frac{3}{4}$ of the pool?

•  $135\pi\ ft^3$  

•  $162\pi\ ft^3$  

•  $180\pi\ ft^3$  

•  $540\pi\ ft^3$  

Which statement best describes how the volume of a square-based pyramid is related to the volume of a cube?

• The volume of a square-based pyramid is $\frac{1}{2}$ the volume of a cube because each face of the cube can be divided into two congruent triangles.

• The volume of a square-based pyramid is $\frac{1}{3}$ the volume of a cube because a cube can be divided into three congruent square-based pyramids.

• The volume of a square-based pyramid is 3 times the volume of a cube because a cube can be divided into three congruent square-based pyramids.

• The volume of a square-based pyramid is 2 times the volume of a cube because each face of the cube can be divided into two congruent triangles.

The entrance to the Louvre Museum in Paris is a square-based pyramid. The volume of the pyramid is $9,039\ m^3$ with a height of 21.6 meters. What is the length of each side of the square base, to the nearest meter?  

•  $29$  

•  $35$  

•  $627$  

•  $1,253$