Multiple Choice Item: 1 point value

Question Overview:This question involves determining the volume of a cone by substituting the appropriate values into the formula. The first step is recognizing that the diameter is given, rather than the radius, requiring you to divide the diameter by 2. After substituting values into the formula, you must convert the result from a mixed number to a decimal. Or, you may convert the mixed number measurements to decimals before subst ituting values into the formula.

Answer Rationale:

Option A is incorrect. If you selected this response, you omitted n from the calculation, which results in V equals one third times eleven eights squared times 4, which is equal to approximately 2.5 cubic inches.

Option B is correct. The paper drinking cup is in the shape of a cone. In order to determine the volume of the cone, you must first find the radius. The diameter of the cone is two and three quarters or eleven quarter inches. Because the radius is half of the diameter, the radius is 11/s inches. You must substitute these and other measurements into the formula for the volume of a cone, which results in V equals one third times pie times eleven eights squared times 4, which is equal to approximately 7.9 cubic inches.

Option C is incorrect. If you selected this response, you omitted one third from the calculation, which results in V equals pie times eleven eights squared times 4, which is equal to approximately 23.7 cubic inches.

Option D is incorrect. If you selected this response, you used the diameter in the calculation of the volume, instead of the radius, which results in V equals one third times pie times eleven fourths squared times 4, which is equal to approximately 31.7 cubic inches.

Formula Sheet

Mathematics Formula Sheet

Area of a:

square A equals s squared

rectangle A equals l w

parallelogram A equals b h

triangle A equals one-half base times height

trapezoid A equals one half h times open parentheses b subscript 1 plus b subscript 2 close parentheses

circle A = pi r squared

Perimeter of a:

square P = 4 s

rectangle P = 2 l plus 2 w

triangle P = side 1 plus side 2 plus side 3

circumference of a circle C = 2 pi r OR C = pi d; pi equals approximately 3 point 1 4

Surface Area and Volume of a:

rectangular prism S A equals 2 l w plus 2 l h plus 2 w h V equals l w h

right prism S A equals p h + 2 B V equals B h

cylinder S A equals 2 pi r h plus 2 pi r squared V equals pi r squared h

pyramid S A equals one half p s + B V equals one third B H

cone S A equals pi r s plus pi r squared V equals one third pi r squared h

sphere S A equals 4 pi r squared V equals 4 thirds pi r cubed

( p = perimeter of base B ; pi is equal to approximately 3.14 )

mean

mean is equal to the total of the values of a data set, divided by the number of elements in the data set

median

median is the middle value in an odd number of ordered values of a data set, or the mean of the two middle values in an even number of ordered values in a data set

data set, or the mean of the two middle values in an even number of ordered values in a data set

Algebra

slope of a line $m equals the fraction, with numerator y subscript 2 minus y subscript 1 and denominator x subscript 2 minus x subscript 1$

slope-intercept form

of the equation of a line y equals m x plus B

point-slope form of the

equation of a line y minus y subscript 1 equals m times open parentheses x minus x subscript 1 close parentheses

standard form of a

quadratic equation y equals a x squared plus b x plus c

quadratic formula $x equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c and denominator 2 a$

Pythagorean Theorem a squared plus b squared equals c squared

simple interest I equals P r t

( I = interest, P = principal, r = rate, t = time)

distance formula d equals r t

total cost Total cost equals number of units times price per unit

Calculator Reference

Basic Arithmetic

To perform basic arithmetic, enter numbers and operation symbols using the standard order of operations. The word “minus” is voiced for the operation of subtraction. The phrase “change sign” is voiced when creating a negative number. To create a negative number, enter the number first, and then press the Change Sign key.

NOTE: To complete all calculations, it is necessary to press the Enter key.

Arithmetic Example 1: Eight times open parentheses negative four close parentheses plus seven equals

The key sequence for this example is voiced by the calculator as follows:

Voiced as:

“Eight, times, four, change sign, plus, seven, enter, negative twenty-five”

The correct answer = -25

Arithmetic Example 2: Zero minus three plus open parentheses negative three close parentheses plus four minus open parentheses negative four close parentheses equals

Voiced as:

“Zero, minus, three, plus, three, change sign, plus, four, minus, four, change sign, enter, two”

The correct answer = 2

Percent

To perform calculations with percent, enter the base number, then use the Percent key.

Percent example: 40 x 560 =

Voiced as:

“Five, six, zero, times, four, zero, percent, enter, two hundred twenty-four”

The correct answer = 224

Scientific Notation

To perform calculations with scientific notation, use the Scientific Notation key. To create a number in scientific notation format, enter the base number. Use the Change Sign key to change the sign if necessary. Press the Scientific Notation key and then enter the numerical exponent. Use the Change Sign key to change the sign of the exponent if necessary.

The answer to calculations involving scientific notation will be given in standard numerical format.

Scientific Notation example: Seven point eight times ten to the eight power minus 1.5 times ten to the eight power equals

Voiced as:

“Seven, point, eight, times ten power, eight, minus, one, point, five, times ten power, eight, enter, six hundred thirty million”

The correct answer = 630000000

Fractions and Mixed Numbers

To perform calculations with fractions and mixed numbers, use the 2nd Function key, followed by the Fraction key. To create a fraction or mixed number, press the 2nd Function key, followed by the Fraction key. The Open Bracket key will automatically appear. Next, enter a whole number (use zero for simple fractions), then press the Comma key. Next, enter the numerator, press the Division key, enter the denominator, and then press the Close Bracket key. The answers to calculations involving fractions and mixed numbers will automatically be formatted in reduced form.

Fraction example: Two ninths times three sevenths equals

Voiced as:

“Second, fraction open bracket, zero, comma, two, divide by, nine, close bracket, times, second, fraction open bracket, zero, comma, three, divide by, seven, close bracket, enter, 2 over 21”

The correct answer = 2/21

Mixed Numbers example: twelve and five sixths minus one and one half equals

Voiced as:

“Second, fraction open bracket, one, two, comma, five, divide by, six, close bracket, minus, second, fraction open bracket, one, comma, one, divide by, two, close bracket, enter, eleven and one-third”

The correct answer = 11 1/3

Powers and Roots

To calculate the square of a number, use the X-Squared / Square Root key. Enter the number, then the X-Squared / Square Root key, then press the Enter key.

Squares example: One point two squared

Voiced as:

“One, point, two, x-squared, enter, one point four four”

The correct answer = 1.44

Powers Other than 2

To calculate powers other than two, use the Power / Nth-Root key. Enter the base number and press the Power / Nth-Root key. Then enter the exponent and press the Enter key

Powers Other than 2 example: Seven to the fourth power equals

Voiced as:

“Seven, power, four, enter, two thousand four hundred one”

The correct answer = 2401

Square Roots

To calculate square roots, use the 2nd Function key and X-Squared / Square Root key. Press the 2nd Function key, and then the X-Squared / Square Root key, followed by the number, then the Enter key.

Square Roots example: Square root of five hundred twenty nine

Voiced as:

“Second, square root of, five, two, nine, enter, twenty-three”

The correct answer = 23

Non-Square Roots

To calculate roots other than square roots, use the 2nd Function key and Y-Power-X / X-Root-Y key. First, enter the numerical root, followed by the 2nd Function key. Then press the Y-Power-X / X-Root-Y key, enter the base number, and press the Enter key.

Non-Square Roots example: Cube root of one thousand seven hundred twenty eight equals

Voiced as:

“Three, second, y-root, one, seven, two, eight, enter, twelve”

The correct answer = 12