Weeks 7&8 - 3D Objects

Which expression represents the volume, in cubic units, of the composite figure?

• $\pi\left(5^2\right)\left(13\right)-\frac{1}{3}\pi\left(5^2\right)\left(12\right)$

• $\pi\left(5^2\right)\left(13\right)-\frac{1}{3}\pi\left(5^2\right)\left(25\right)$

• $\pi\left(5^2\right)\left(13\right)+\frac{1}{3}\pi\left(5^2\right)\left(12\right)$

• $\pi\left(5^2\right)\left(13\right)+\frac{1}{3}\pi\left(5^2\right)\left(25\right)$

What is the volume of the composite figure? Express answer in terms of  $\pi$  . 

•  $144\pi\ mm^3$  

•  $168\pi\ mm^3$  

•  $312\pi\ mm^3$  

•  $456\pi\ mm^3$  

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or square prism. The company wants to use the package that has the least amount of wasted space. The company should choose:

• the prism because it has approximately 11.6 in³ less wasted space than the cylinder.

• the prism because it has approximately 14.1 in³ less wasted space than the cylinder.

• the cylinder because it has approximately 11.6 in³ less wasted space than the prism.

• the cylinder because it has approximately 14.1 in³ less wasted space than the prism.

A solid oblique cone with a slant height of 17 units is placed inside an empty cylinder with a congruent base radius of 8 units and height of 15 units. What is the unfilled volume inside the cylinder?

• $320\pi\ \ units^3$

• $597\pi\ \ units^3$

• $640\pi\ \ units^3$

• $725\pi\ \ units^3$

A solid right pyramid has a regular hexagonal base with an area of 7.4 units². The pyramid has a height of 6 units. To the nearest tenth, what is the volume of the pyramid?

• 11.1 units³

• 14.8 units³

• 22.2 units³

• 44.4 units³

The volume of the triangular block is 4 cubic inches. What is the approximate length of y? Round to the nearest tenth of an inch.

• 1.4 in

• 2.0 in

• 2.8 in

• 3.5 in

What is the volume of the shaded portion of the composite figure? Express your answer in terms of π.

• $519\pi\ units^3$

• $681\pi\ units^3$

• $\left(600\pi-81\right)\ units^3$

• $\left(600-81\pi\right)\ units^3$

The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units.

What is the height of the cylinder?

• 2 units

• 4 units

• 6 units

• 8 units

A three-dimensional model of Lucia’s apartment is shown. To cool the whole apartment, an air conditioner must provide 2.5 BTUs per cubic foot. How many BTUs are needed to cool Lucia’s apartment?

• 3,264 BTUs

• 8,160 BTUs

• 20,400 BTUs

• 24,000 BTUs

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter.

• 1,005 cm³

• 1,340 cm³

• 3,351 cm³

• 4,021 cm³