Adora has a photo of the Calgary tower that measures 7cm by 19cm. She scans the photo and enlarges it by 160%. By what percentage will the area of the photo increase?
A.) 160%
B.) 320%
C.) 410%
D.) 256%
A shop sells a small globe that hangs on a keychain, a medium globe used as a paperweights 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 medium globes.
A.) k=6^3
B.) k=root 6
C.) k=6
D.) k=^3root6
A gift shop in Cairo sells a tiny pyramid pendant. Due to its popularity,the shop decided to make two larger, yet similar versions: medium(double the volume of the tiny one) and large(triple the volume of the tiny one). What is the factor relating the surface area of the tiny pyramid to the surface area of the medium pyramid? (the pyramids dimensions are 1 cm by 1 cm by 1 cm).
A.) 4
B.) ^3root4
C.) ^6root2
D.) 8
Thanks so much
To find the answers to these questions, we need to use some basic mathematical formulas and concepts. Let's solve each question step-by-step.
1. The first question is about the enlargement of a photo. The photo's dimensions are given as 7cm by 19cm. We need to find the increase in its area after enlarging it by 160%.
To calculate the area of the original photo, we multiply its length and width:
Area of original photo = 7cm x 19cm = 133cm²
Next, we need to determine the new dimensions after enlarging by 160%. To find the increase percentage, we add 100% to the enlargement percentage:
Total percentage increase = 100% + 160% = 260%
To calculate the new dimensions, we multiply the original dimensions by 260% (or 2.6):
New length = 7cm x 2.6 = 18.2cm
New width = 19cm x 2.6 = 49.4cm
Finally, we calculate the area of the enlarged photo by multiplying the new length and width:
Area of enlarged photo = 18.2cm x 49.4cm = 898.28cm²
To find the percentage increase in area, we compare the original area to the enlarged area:
Percentage increase in area = (Area of enlarged photo - Area of original photo) / Area of original photo x 100%
= (898.28cm² - 133cm²) / 133cm² x 100%
= 675.28cm² / 133cm² x 100%
= 507.34%
Therefore, the area of the photo will increase by approximately 507.34%. The closest answer option is C.) 410%.
2. The second question involves determining the scale factor relating the dimensions of the small and medium globes.
Let's assume the dimensions of the small globe are x.
The volume of the medium globe is six times the volume of the small globe, so its dimensions would be 6x.
Similarly, the volume of the large globe is nine times the volume of the small globe, so its dimensions would be 9x.
The scale factor is the ratio of the dimensions of the small and medium globes.
k = (dimensions of medium globe) / (dimensions of small globe)
k = 6x / x
k = 6
Therefore, the scale factor relating the dimensions of the small and medium globes is 6. The answer is C.) 6.
3. The third question involves finding the factor relating the surface area of a tiny pyramid to the surface area of the medium pyramid.
The dimensions of the tiny pyramid are given as 1 cm by 1 cm by 1 cm. This means each side of the tiny pyramid is 1 cm.
To calculate the surface area of a pyramid, we need to determine the area of each side and then sum them up.
The surface area of the tiny pyramid is given by:
Surface area = (area of base) + (area of each side)
The base is a square with sides of length 1 cm, so its area is 1 cm x 1 cm = 1 cm².
Each side of the tiny pyramid is also a square with sides of length 1 cm, so the area of each side is 1 cm x 1 cm = 1 cm².
Therefore, the surface area of the tiny pyramid is: Surface area = 1 cm² + 1 cm² + 1 cm² + 1 cm² = 4 cm².
Now, let's consider the medium pyramid. We are given that the volume of the medium pyramid is double the volume of the tiny pyramid.
Since the shape of a pyramid is similar regardless of its size, the ratio of the surface areas is equal to the square of the ratio of their side lengths.
If the volume is doubled, the side length will be ∛2 times the side length of the tiny pyramid.
Therefore, the factor relating the surface area of the tiny pyramid to the surface area of the medium pyramid is (∛2)² = 2.
Therefore, the answer is A.) 2.
I hope this helps! Let me know if you have any further questions.