For the roof of the shelter, Mia has a board that measures 1 square yard, a second
board that measures 3 feet by 3 feet, and a third board that measures 36 inches by
36 inches. Which of these, if any, will cover all the space needed for the roof?
Explain your answer, drawing a picture if necessary.
1 foot = 1/3 of a yard
To determine if any of the boards will cover all the space needed for the roof, we need to compare their sizes.
1 square yard is equal to 3 feet by 3 feet (since 1 yard = 3 feet).
The second board measures 3 feet by 3 feet, which is the same as 1 square yard. Therefore, this board will cover all the space needed for the roof.
The third board measures 36 inches by 36 inches. Since 1 foot is equal to 1/3 of a yard, 36 inches is equal to 1/3 of a yard as well. So, the third board also measures 1 square yard and will cover all the space needed for the roof just like the second board.
In conclusion, both the second and third boards will cover all the space needed for the roof.
To determine which board can cover all the space needed for the roof, let's convert the measurements into a consistent unit, either yards or inches.
Given:
1 foot = 1/3 yard
First, let's convert the second board's measurements from feet to yards:
Since each side of the second board measures 3 feet, we can calculate the length in yards by dividing by 3:
3 feet ÷ 3 = 1 yard
So, the second board measures 1 yard by 1 yard.
Next, let's convert the third board's measurements from inches to yards:
Since there are 36 inches in a yard, we can calculate the length in yards by dividing by 36:
36 inches ÷ 36 = 1 yard
So, the third board measures 1 yard by 1 yard.
Now, we have the following measurements in yards:
- First board: 1 square yard
- Second board: 1 yard by 1 yard
- Third board: 1 yard by 1 yard
Looking at the measurements, all three boards have the same area, which is 1 square yard. Therefore, any of these three boards can cover all the space needed for the roof.
Please note that a visual representation of the boards would have been helpful, but as an AI text-based bot, I am unable to draw pictures.
To determine which board will cover all the space needed for the roof, we need to compare the areas of the boards to the area needed for the roof.
First, let's convert the measurements to a common unit for easier comparison.
Since 1 yard is equal to 3 feet, we can convert the yard measurement of the first board to feet by multiplying it by 3. So the first board measures 1 yard * 3 feet/yard = 3 feet.
Now, let's calculate the areas:
- The first board has an area of 3 feet * 3 feet = 9 square feet.
- The second board is already given in square feet and has an area of 3 feet * 3 feet = 9 square feet.
- The third board has an area of 36 inches * 36 inches = 1296 square inches. To convert this to square feet, we divide by 12 squared (since there are 12 inches in a foot), which gives us 1296 square inches / (12 inches/foot)^2 = 9 square feet.
As we can see, all three boards have the same area of 9 square feet. Therefore, any of these boards will cover all the space needed for the roof.
To visualize this, we can draw a simple rectangle with dimensions 3 feet by 3 feet, representing the area needed for the roof. Then, we can draw three squares with dimensions 3 feet by 3 feet, representing the dimensions of each board. All three squares will fit perfectly within the rectangle, showing that all the boards will cover the space needed for the roof.
It's important to note that drawing a picture is just one way to help visualize the problem. The key step is to compare the areas of the boards to the area needed for the roof, which can be done by converting the measurements to a common unit.
Roger is planning a party. He needs these ingredients in the following quantities to
make punch:
• 2 quarts orange juice
• 3 cups cranberry juice
• 1 gallon ginger ale
• 1 pint pineapple juice
Roger knows he will need a relatively large container to mix the punch.
Unfortunately, all he can find is a bowl that holds 8 liters of liquid. He is not sure
whether he can fit all of the ingredients in the bowl at the same time.
Use the following measurement equivalents to determine if Roger can use the 8-
liter bowl to mix all the ingredients for the punch. Show your work.
If he can use the bowl, he needs to determine how many liters of liquid could still
fit into the bowl. If he cannot use the bowl, he needs to determine how many extra
liters of liquid there are. Round your answers to the nearest tenth of a liter.
1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to calculate the total volume of the ingredients he needs.
Given ingredient quantities:
- 2 quarts orange juice = 2.12 liters (since 1 quart is approximately equal to 0.95 liters)
- 3 cups cranberry juice = 0.71 liters (since 3 cups is approximately equal to 0.71 liters)
- 1 gallon ginger ale = 3.79 liters (since 1 gallon is approximately equal to 3.79 liters)
- 1 pint pineapple juice = 0.47 liters (since 1 pint is approximately equal to 0.47 liters)
Now, let's calculate the total volume of the ingredients:
2.12 liters + 0.71 liters + 3.79 liters + 0.47 liters = 7.09 liters
The total volume of the ingredients needed is approximately 7.09 liters.
Since the 8-liter bowl can hold more than 7.09 liters, Roger can use the bowl to mix all the ingredients for the punch.
To determine how many liters of liquid could still fit into the bowl, we can subtract the total volume of the ingredients from the capacity of the bowl:
8 liters - 7.09 liters = 0.91 liters
Therefore, approximately 0.91 liters of liquid could still fit into the bowl.
In summary, Roger can use the 8-liter bowl to mix all the ingredients for the punch, and approximately 0.91 liters of liquid could still fit into the bowl.
make it shorter please
Roger can use the 8-liter bowl to mix all the ingredients for the punch. He would have approximately 0.91 liters of space left in the bowl.
not that short a little longer like 121 words
Roger can use the 8-liter bowl to mix all the ingredients for the punch. The total volume of the ingredients needed is approximately 7.09 liters. Since the 8-liter bowl can hold more than 7.09 liters, it is large enough for the punch. After combining all the ingredients, there would be approximately 0.91 liters of space left in the bowl. Roger can use this extra space for ice or decorations.
Roger also wants to make sandwiches for his guests. He buys the following
sandwich fillings:
• 1.5 kilograms of turkey
• 1.25 kilograms of beef
• 2.25 pounds of cheese
Roger wants to know if he purchased more turkey or more cheese. Use the
conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer.
Show your work.