Resources

Resources

Volume of cubes and rectangular prisms: word problems

An object is launched from a platform.

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Its height (in meters),

x

seconds after the launch, is modeled by:

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h(x)=-5x^{2}+20x+60

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What is the height of the object at the time of launch?

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\square

A laundry detergent box measures

12

8

2\frac{1}{2}

inches. What is the volume of two boxes of detergent?

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490\text{in}^3

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480\text{in}^3

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450\text{in}^3

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500\text{in}^3

Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of

15\,\text{cm}

, and the smaller mug has an internal height of

10\,\text{cm}

. Both mugs have an internal diameter of

8\,\text{cm}

. Which of the following is closest to the difference in cubic centimeters

(\text{cm}^3)

between the internal volume of the larger mug and the internal volume of the smaller mug?

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1

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63\,\text{cm}^3

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251\,\text{cm}^3

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754\,\text{cm}^3

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1,005\,\text{cm}^3

The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method:

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3.15 \times 10^{-3}

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8.5 \times 10^{-4}

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How many times larger is the diameter of cell

\mathrm{K}

than the diameter of cell

\mathrm{M}

? Write your answer in standard notation, rounding to the nearest tenth.

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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is

34

centimeters. Find the length and width of the rectangle.

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\text { Width }=\square \text { centimeters } \quad \text { Length }=\square \text { centimeters }

The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is

48

centimeters. Find the length and width of the rectangle.

\newline

\text { Width }=\square \text { centimeters } \quad \text { Length }=\square \text { centimeters }

The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is

80

feet. Find the length and width of the rectangle.

\newline

\text { Width }=\square \text { feet } \text { Length }=\square \text { feet }

A rectangular prism has a length of

12

\text{in}

, a height of in, and a width of

8

\text{in}

. What is its volume, in cubic in?

\newline

V=\square

\text{in}

^{3}

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

h

, in meters, after

b

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1

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h=4\cdot0.79^{(b-1)}

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h=4\cdot0.79^{b}

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h=4-0.79\cdot b^{2}

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h=4\cdot(1-0.79\cdot b^{2})

Imani's grandmother's house is

5

miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at

10

miles per hour. Which equation best describes the distance,

\newline

d

, in miles, Imani is from home after

\newline

t

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1

\newline

d=5+10t

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d=5-10t

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d=5t+10

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d=5t-10

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

\newline

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

\newline

h

, in meters, after

\newline

b

\newline

1

\newline

\newline

h=4\cdot0.79^{(b-1)}

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h=4\cdot0.79^{b}

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h=4-0.79\cdot b^{2}

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h=4\cdot(1-0.79\cdot b^{2})

A contractor is to build a new structure at a farm for seed storage. It will have a rectangular base, which is

20

35

feet long, with walls of thickness

t

feet. The structure is

90

feet tall. Excluding the volume of the walls, which of the following functions best models the volume,

V

, in cubic feet, inside the structure?

Chinedu was given this problem:

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A person stands at a distance of

18

meters east of an intersection and watches a car driving away from the intersection to the north at

3

meters per second. The function

y(t)

gives the car's distance, in meters, north of the intersection at time

t

. At a certain instant

t_{0}

\theta\left(t_{0}\right)

between the line of sight from the person to the car and the line of sight from the person to the intersection is

0

7

radians. What is the rate of change of the angle

\theta(t)

at that instant?

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Which equation should Chinedu use to solve the problem?

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1

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\tan [\theta(t)]=\frac{y(t)}{18}

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\theta(t)=\frac{18 \cdot y(t)}{2}

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\theta(t)+18+y(t)=180

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[\theta(t)]^{2}=18^{2}+[y(t)]^{2}

Steve was given this problem:

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r(t)

of a circle is increasing at a rate of

3

centimeters per second. At a certain instant

t_{0}

, the radius is

8

centimeters. What is the rate of change of the area

A(t)

of the circle at that instant?

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Which equation should Steve use to solve the problem?

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1

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A(t)=2 \pi \cdot r(t)

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A(t)=\pi[r(t)]^{2}

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A(t)=4 \pi[r(t)]^{2}

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A(t)=\frac{4}{3} \pi[r(t)]^{3}