5 of 55 of 5 Items
16:16
Question
A model of the bean bag toss board that Scott made is shown. The eyes, nose, and mouth are holes cut in the board.
Which measurement is the best estimate of the area of the board that is left after the holes are cut for the eyes, nose, and mouth? Use 3 for pi. Use paper and pencil to find the answer.
Responses
A
9 5 ft2
89 5 ft 2 8
B
6 3 ft2
86 3 ft 2 8
C
7 3 ft2
87 3 ft 2 8
D
5 1 ft2
45 1 ft 2 4
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To find the best estimate of the area of the board left after the holes are cut, we need to calculate the areas of the holes and subtract them from the total area of the board.
Based on the given model, it looks like there are three holes - two eyes and a mouth. Let's calculate the area of each hole and then subtract them from the total area.
The area of a circle is given by the formula A = πr^2, where π is approximately 3 and r is the radius of the circle.
Looking at the model, it appears that the radius of each eye hole is approximately 1 foot. Therefore, the area of each eye hole is approximately A = 3(1^2) = 3 square feet.
The mouth hole appears to be a semi-circle. The formula for the area of a semi-circle is A = (πr^2)/2. Since the radius of the mouth hole also appears to be approximately 1 foot, the area of the mouth hole is approximately A = (3(1^2))/2 = 1.5 square feet.
Now, we need to subtract the areas of the holes from the total area of the board. The total area of the board is given by the formula A = length x width.
Looking at the model, it appears that the length of the board is approximately 5 feet and the width is approximately 5 feet. Therefore, the total area of the board is approximately A = 5 x 5 = 25 square feet.
Now let's subtract the areas of the holes from the total area of the board:
Total area of the board - Area of eye holes - Area of mouth hole
25 - (2 x 3) - 1.5
25 - 6 - 1.5
18.5
Therefore, the best estimate of the area of the board that is left after the holes are cut is approximately 18.5 square feet.
The closest answer choice to 18.5 square feet is option D) 5 1/4 ft^2.
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6 of 66 of 6 Items
17:21
Question
Brian grilled a hamburger. The diameter of the hamburger was 5 cm. What was the area of burger?
Responses
A 15.7 cm²15.7 cm²
B 78.5 cm²78.5 cm²
C 19.625 cm²19.625 cm²
D 12.56 cm²
To find the area of the hamburger, we need to use the formula for the area of a circle, which is A = πr^2, where π is approximately 3.14 and r is the radius of the circle.
In this case, the diameter of the hamburger is given as 5 cm. The radius is half of the diameter, so the radius of the hamburger is 5/2 = 2.5 cm.
Now we can calculate the area of the hamburger:
A = 3.14(2.5^2)
A = 3.14(6.25)
A ≈ 19.625 cm²
Therefore, the correct answer is option C) 19.625 cm².
7 of 77 of 7 Items
17:46
Question
A circular drum has a radius of 12.25 inches. Karen wants to glue a ribbon around the edge of the drum. If Karen has exactly enough ribbon, which measurement is closest to the length of the piece of ribbon in inches?
Responses
A 38.465 inches38.465 inches
B 24.50 inches24.50 inches
C 76.93 inches76.93 inches
D 36.74 inches
To find the length of the ribbon needed to go around the circular drum, we need to use the formula for the circumference of a circle, which is C = 2πr, where π is approximately 3.14 and r is the radius of the circle.
In this case, the radius of the drum is given as 12.25 inches.
Now we can calculate the circumference of the drum:
C = 2(3.14)(12.25)
C = 6.28(12.25)
C ≈ 76.93 inches
Therefore, the closest measurement to the length of the ribbon needed is option C) 76.93 inches.
8 of 88 of 8 Items
18:22
Question
The dimensions of a triangular prism are shown in the diagram. The prism is not drawn to scale.
What is the volume of the triangular prism in cubic centimeters?
Responses
A 302,400 cm³302,400 cm³
B 121,500 cm³121,500 cm³
C 250,000 cm³250,000 cm³
D 151,200 cm³
To find the volume of a triangular prism, we need to use the formula V = (1/2)bhA, where b is the base of the triangle, h is the height of the triangle, and A is the depth (or length) of the prism.
Looking at the diagram, we can see that the base of the triangle is 16 centimeters and the height is 9 centimeters. Therefore, the area of the triangle is (1/2)(16)(9) = 72 square centimeters.
The depth (or length) of the prism is given as 350 centimeters.
Now we can calculate the volume of the prism:
V = (1/2)(16)(9)(350)
V = 72(350)
V = 25,200 cubic centimeters.
Therefore, the volume of the triangular prism is 25,200 cubic centimeters.
The correct answer is not among the given answer choices.
What is the volume of the object above if each cube is 1 cubic inch?
Responses
A 72 in.³72 in.³
B 60 in.³60 in.³
C 66 in.³66 in.³
D 48 in.³