Verified answer

Step-by-step explanation:

1. The surface area of the cube is 294 square cm.

Solution: The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that result by 6 (since there are 6 faces on a cube).

Surface area = 6 x side^2

Surface area = 6 x side^2Surface area = 6 x 7^2

Surface area = 6 x side^2Surface area = 6 x 7^2Surface area = 6 x 49

Surface area = 6 x side^2Surface area = 6 x 7^2Surface area = 6 x 49Surface area = 294 square cm

2. Matilda needs 800 square inches of gift wrapper to wrap the entire box.

Solution: The surface area of a rectangular prism can be found by using the formula:

Surface area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

Surface area = 2(20 x 15) + 2(20 x 5) + 2(15 x 5)

Surface area = 2(20 x 15) + 2(20 x 5) + 2(15 x 5)Surface area = 600 + 200 + 150

Surface area = 2(20 x 15) + 2(20 x 5) + 2(15 x 5)Surface area = 600 + 200 + 150Surface area = 950 square inches

Therefore, Matilda needs 950 square inches of gift wrapper to wrap the entire box.

3. The surface area of the tumbler is approximately 471 square cm.

Solution: The surface area of a cylinder can be found by using the formula:

Surface area = 2πr^2 + 2πrh

where r is the radius, and h is the height.

Surface area = 2π(5)^2 + 2π(5)(25)

Surface area = 2π(5)^2 + 2π(5)(25)Surface area = 2π(25) + 2π(125)

Surface area = 2π(5)^2 + 2π(5)(25)Surface area = 2π(25) + 2π(125)Surface area = 50π + 250π

Surface area = 2π(5)^2 + 2π(5)(25)Surface area = 2π(25) + 2π(125)Surface area = 50π + 250πSurface area = 300π

Surface area = 2π(5)^2 + 2π(5)(25)Surface area = 2π(25) + 2π(125)Surface area = 50π + 250πSurface area = 300πSurface area ≈ 942.48 square cm (rounded to two decimal places)

Therefore, the surface area of the tumbler is approximately 471 square cm.

4. Approximately 962 square cm of colored paper would be needed to create the hat.

Solution: The surface area of a cone can be found by using the formula:

Surface area = πr^2 + πrl

where r is the radius, and l is the slant height.

First, we need to find the height of the cone by using the Pythagorean theorem:

h^2 = l^2 - r^2

h^2 = l^2 - r^2h^2 = 18^2 - 10^2

h^2 = l^2 - r^2h^2 = 18^2 - 10^2h^2 = 324 - 100

h^2 = l^2 - r^2h^2 = 18^2 - 10^2h^2 = 324 - 100h^2 = 224

h ≈ 14.97 cm (rounded to two decimal places)

Now we can find the surface area of the cone:

Surface area = π(10)^2 + π(10)(14.97)

Surface area = π(100) + π(149.7)

Surface area = 314.16 + 471.24

Surface area ≈ 785.40 square cm (rounded to two decimal places)

Since the cone is made from a single sheet of colored paper, we also need to account for the circular base of the cone:

Area of base = πr^2

Area of base = π(10)^2

Area of base = 100π

Total area of colored paper needed = Surface area + Area of base

Surface area + Area of baseTotal area of colored paper needed ≈ 785.40 + 100π

Surface area + Area of baseTotal area of colored paper needed ≈ 785.40 + 100πTotal area of colored paper needed ≈ 962.03 square cm (rounded to two decimal places)

Therefore, approximately 962 square cm of colored paper would be needed to create the hat.

5. The surface area of the table tennis ball is approximately 2,011 square mm.

Solution: The surface area of a sphere can be found by using the formula:

Surface area = 4πr^2

where r is the radius.