Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?
(1 point)
Responses
30 square centimeters
30 square centimeters
33 square centimeters
33 square centimeters
39 square centimeters
39 square centimeters
27 square centimeters
The total area of the piece of jewelry can be calculated as the sum of the areas of the individual shapes, which are a rectangle and two semicircles.
Area of rectangle = length * width = 9 * 3 = 27 square cm
Area of one semicircle = (1/2) * π * r^2 = 0.5 * π * 2^2 = 2π square cm
Total area = 27 + 2π + 2π = 27 + 4π
Since π is approximately 3.14:
Total area ≈ 27 + 4 * 3.14 = 27 + 12.56 = 39.56 square cm
Therefore, the total area of the piece of jewelry is approximately 39.56 square centimeters. So the closest option is 39 square centimeters.
Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?(1 point)
feet
In the supply closet shown in the image, we can see that it is a rectangle. The total area of the closet is given as 36 square feet.
To find the length of the side labeled with the question mark (let's call it x), we can set up the equation:
Area = length * width
36 = x * 6
x = 36/6
x = 6
Therefore, the length of the side of the supply closet labeled with the question mark is 6 feet.
Ethan writes the ratio x8=y16 to help him reduce the size of a two-dimensional shape. If the new value of y is 3 units, what will be the value of x ?(1 point)
Responses
1.5 units
1.5 units
6 units
6 units
316 units
Start Fraction 3 over 16 End Fraction units
0.5 units
To find the value of x in the ratio x:8 = y:16, we can use proportions since the ratio x:8 is equivalent to y:16 in this case.
Given that y = 3 units, we can set up the proportion:
x/8 = 3/16
Cross multiplying, we get:
16x = 8 * 3
16x = 24
Dividing by 16 from both sides, we get:
x = 24 / 16
x = 1.5 units
Therefore, the value of x is 1.5 units.
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?(1 point)
Responses
1.5 inches by 1 inch
1.5 inches by 1 inch
1 inch by 0.5 inches
1 inch by 0.5 inches
2 inches by 1 inch
2 inches by 1 inch
12 inches by 8 inches
To find a smaller scale drawing of the original printed photograph, we must reduce the original dimensions proportionally. The original dimensions are 6 inches by 4 inches.
Let's find the scale factor first:
Original width: 6 inches
Smaller width: x inches
Scale factor = x / 6
Original height: 4 inches
Smaller height: y inches
Scale factor = y / 4
Typically, we select a scale factor that both x and y share. Let's choose 1.5 for both x and y.
New dimensions:
Width = 6 inches / 1.5 = 4 inches
Height = 4 inches / 1.5 = 2.67 inches
None of the options exactly match these dimensions, but the closest option is:
2 inches by 1 inch
Therefore, 2 inches by 1 inch represents a smaller scale drawing of the original printed photograph.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
(1 point)
Responses
20 square inches
20 square inches
3.2 square inches
3.2 square inches
6.4 square inches
6.4 square inches
1.6 square inches
To find the area of Crystal's scale drawing of the triangle, we need to calculate the scale factor by comparing the heights of the original triangle and the scale drawing.
Scale factor = height of scale drawing / height of original triangle
Scale factor = 2 / 5
Scale factor = 0.4
Now, we can use the scale factor to find the base of the scale drawing:
Base of the scale drawing = Scale factor * base of original triangle
Base of the scale drawing = 0.4 * 8
Base of the scale drawing = 3.2 inches
Now that we have the base and height of the scale drawing, we can find its area:
Area of the scale drawing = (1/2) * base * height
Area of the scale drawing = (1/2) * 3.2 * 2
Area of the scale drawing = 3.2 square inches
Therefore, the area of Crystal's scale drawing is 3.2 square inches.