Question

Leeor was asked to repaint the sign for his mother's ice cream shop, so he needs to figure out how much paint he will need. Determine the area of the ice cream cone on the sign. Round to the nearest tenth.

Answer 1

the area is approximately 50.1 square inches.

To determine the area of the ice cream cone on the sign, we need to calculate the area of the semicircle (which represents the ice cream) and the area of the triangle (which represents the cone).

1. Area of the Semicircle:

The formula for the area of a circle is
`\( A = \pi r^2 \)`. For a semicircle (half of a circle), the area is half of that.

Given the diameter is 6 inches, the radius
`\( r \)` is half of that, which is 3 inches.

`\( \text{Area of semicircle} = (1)/(2) \pi r^2 = (1)/(2) \pi (3^2) \)`

`\( \text{Area of semicircle} = (1)/(2) \pi (9) \)`

`\( \text{Area of semicircle} = (9)/(2) \pi \)`

2. Area of the Triangle:

The formula for the area of a triangle is
`\( A = (1)/(2) * \text{base} * \text{height} \).`

For the triangle, the base is equal to the diameter of the semicircle, which is 6 inches, and the height is given as 12 inches.

`\( \text{Area of triangle} = (1)/(2) * 6 * 12 \)`

`\( \text{Area of triangle} = 3 * 12 \)`

`\( \text{Area of triangle} = 36 \)`

Now, we can add the two areas together to find the total area of the ice cream cone:

`\( \text{Total area} = \text{Area of semicircle} + \text{Area of triangle} \)`

`\( \text{Total area} = (9)/(2) \pi + 36 \)`

Since
`\( \pi \)` is approximately 3.1416, we can calculate the total area as follows:

`\( \text{Total area} \approx (9)/(2) * 3.1416 + 36 \)`

`\( \text{Total area} \approx 14.1372 + 36 \)`

`\( \text{Total area} \approx 50.1372 \)`

Rounded to the nearest tenth, the area is approximately 50.1 square inches.

Leeor will need enough paint to cover this area on the sign.

Answer 2

we can split the figure into two parts and then add its area

for the circle area

`A_1=(\pi* r^2)/(2)`

where r is 3 because is half the diameter,

and we divide the area in half since it is half a circle

so

`\begin{gathered} A_1=(\pi*3^2)/(2) \\ A_1=(9\pi)/(2)\approx14.137 \end{gathered}`

for the triangle area