Jerry wants to wrap a present in a box for his mother. The box measures 10 cm wide, 4 cm high, and 17 cm long. How much wrapping paper will Jerry need to wrap the present?
To wrap the present, Jerry will need to cover the surface area of the box. The surface area of a box can be calculated by finding the area of each face and adding them together.
The box has six faces:
- Top: 10 cm x 17 cm = 170 cm²
- Bottom: 10 cm x 17 cm = 170 cm²
- Front and back: 4 cm x 17 cm = 68 cm² each, for a total of 136 cm²
- Left and right sides: 4 cm x 10 cm = 40 cm² each, for a total of 80 cm²
To find the total surface area, we add up all the areas:
170 cm² + 170 cm² + 136 cm² + 80 cm² + 80 cm² + 136 cm² = 772 cm²
Therefore, Jerry will need 772 cm² of wrapping paper to wrap the present.
To determine how much wrapping paper Jerry will need, we need to calculate the surface area of the box.
Step 1: Calculate the area of the bottom of the box.
The area of the bottom of the box is equal to the length multiplied by the width.
Area = length * width
Area = 17 cm * 10 cm
Area = 170 cm^2
Step 2: Calculate the area of one of the sides of the box.
The area of one side of the box is equal to the height multiplied by the width. Since there are two sides with the same dimensions, we will calculate it only once.
Area = height * width
Area = 4 cm * 10 cm
Area = 40 cm^2
Step 3: Calculate the area of the other side of the box.
Since there are two sides with the same dimensions, the calculation will be the same as in Step 2.
Area = 4 cm * 10 cm
Area = 40 cm^2
Step 4: Calculate the area of the front and back sides of the box.
The area of the front and back sides is equal to the length multiplied by the height. Since there are two sides with the same dimensions, we will calculate it only once.
Area = length * height
Area = 17 cm * 4 cm
Area = 68 cm^2
Step 5: Calculate the total surface area of the box.
The total surface area is equal to the sum of all the areas calculated in the previous steps.
Total Surface Area = 2 * (Area of bottom) + 2 * (Area of one side) + 2 * (Area of front and back)
Total Surface Area = 2 * 170 cm^2 + 2 * 40 cm^2 + 2 * 68 cm^2
Total Surface Area = 340 cm^2 + 80 cm^2 + 136 cm^2
Total Surface Area = 556 cm^2
Therefore, Jerry will need 556 cm^2 of wrapping paper to wrap the present.