Adolph, a dolphin at a zoo, is 7 m long. A stuffed animal version of Adolph is sold in the gift shop. If the scale factor used to reduce the real Adolph to the stuffed animal Adolph is 0.06, how tall is the stuffed animal Adolph?
Select one:
a.
42 cm
b.
117 cm
c.
117 m
d.
42 m
To find the height of the stuffed animal Adolph, we need to multiply the scale factor by the length of the real Adolph.
Scale factor x Length of Adolph = Height of stuffed animal Adolph
0.06 x 7m = 0.42m
Therefore, the stuffed animal Adolph is 42 cm tall.
The answer is: a. 42 cm
Carly drew a scale diagram of Calgary Tower. The height of the actual tower is 191 m. The height in Carly’s diagram is 38.2 cm.
Determine the scale factor of the diagram.
Select one:
a.
0.02
b.
0.002
c.
5
d.
0.5
To find the scale factor, we divide the height in Carly's diagram by the actual height of the tower.
Scale factor = Height in diagram / Actual height
Scale factor = 38.2 cm / 191 m
First, convert cm to m by dividing by 100:
Scale factor = (38.2 cm / 100) / 191 m
Simplify:
Scale factor = 0.382 / 191
Scale factor = 0.002
Therefore, the scale factor of the diagram is 0.002.
The answer is: b. 0.002
Adora has a photo of the Calgary Tower that measures 7 cm by 19 cm. She scans the photo and enlarges it by 160%. What are the minimum inside dimensions of the frame he will need for the enlarged photo?
Select one:
a.
1120 cm by 3040 cm
b.
11.2 cm by 30.4 cm
c.
437.5 cm by 1187.5 cm
d.
4.4 cm by 11.9 cm
To find the dimensions of the enlarged photo, we need to multiply the original dimensions by the enlargement percentage.
Enlarged width = Original width x Enlargement percentage
Enlarged height = Original height x Enlargement percentage
Original width = 7 cm
Original height = 19 cm
Enlargement percentage = 160% = 1.6
Enlarged width = 7 cm x 1.6 = 11.2 cm
Enlarged height = 19 cm x 1.6 = 30.4 cm
Therefore, the minimum inside dimensions of the frame Adora will need for the enlarged photo are 11.2 cm by 30.4 cm.
The answer is: b. 11.2 cm by 30.4 cm
Adora has a photo of the Calgary Tower that measures 7 cm by 19 cm. She scans the photo and enlarges it by 160%. By what percentage will the area of the photo increase?
Select one:
a.
256%
b.
410%
c.
160%
d.
320%
To find the percentage increase in area, we need to calculate the ratio of the new area to the original area.
Original area = 7 cm * 19 cm = 133 cm^2
Enlarged area = (7 cm * 1.6) * (19 cm * 1.6) = 17.92 cm * 30.4 cm = 545.728 cm^2
Percentage increase = (Enlarged area - Original area) / Original area * 100
Percentage increase = (545.728 cm^2 - 133 cm^2) / 133 cm^2 * 100
Percentage increase = 412.728 cm^2 / 133 cm^2 * 100
Percentage increase ≈ 310.18%
Therefore, the area of the photo will increase by approximately 310.18%.
The answer is not provided in the options.
A shop sells a small globe that hangs on a keychain, a medium globe used as a paperweight, and a large globe for use in the classroom. The volume of the medium globe is six times the volume of the small globe and the volume of the large globe is nine times the volume of the small globe.
Determine the scale factor relating the dimensions of the small and large globes.
Select one:
a. k=9^2
b. k=cube sqrt 9
c. k=sqrt9
d. k=9
To determine the scale factor relating the dimensions of the small and large globes, we can use the relationship between volumes.
Since volume is a measure of the space occupied by an object, it is directly proportional to the cube of the scale factor.
In this case, the volume of the large globe is nine times the volume of the small globe. Therefore, the scale factor relating the dimensions of the small and large globes can be found by taking the cube root of 9.
Scale factor = cube root of 9 = ∛9
Since ∛9 is not one of the given options, it seems that none of the options provided are correct.
A shop sells a small globe that hangs on a keychain, a medium globe used as a paperweight, and a large globe for use in the classroom. The volume of the medium globe is six times the volume of the small globe and the volume of the large globe is nine times the volume of the small globe.
What is the factor relating the surface area of the small globe to the surface area of the large globe?
Select one:
a. 6^sqrt9
b. 3 cube sqrt3
c. 729
d. 81