1. The decorative icing around the top edge of a circular cake measures approximately 25.12 inches in length. How much icing is needed to cover the entire top of the cake? $$ 25.12 \mathrm{in} .^{2} $$ $$ 50.24 \mathrm{in.}^{2} $$ $$ 247.67 \mathrm{in} .^{2} $$ $$ 200.96 \mathrm{in.}^{2} $$

Question

UpStudy AI · Accepted Answer

To determine how much icing is needed to cover the entire top of the cake, follow these steps:

1. **Understand the Given Information:**
   - The length of the decorative icing around the top edge of the cake is the circumference of the cake, which is $$ 25.12 $$ inches.

2. **Find the Radius of the Cake:**
   - The formula for the circumference ($$ C $$) of a circle is:
     $$
     C = 2\pi r
     $$
     Where $$ r $$ is the radius.
     
   - Solving for $$ r $$:
     $$
     r = \frac{C}{2\pi} = \frac{25.12}{2 \times 3.1416} \approx 4 \text{ inches}
     $$

3. **Calculate the Area of the Top of the Cake:**
   - The area ($$ A $$) of a circle is given by:
     $$
     A = \pi r^2
     $$
     
   - Substituting the radius:
     $$
     A = 3.1416 \times 4^2 = 3.1416 \times 16 \approx 50.27 \text{ in}^2
     $$
     
4. **Select the Closest Option:**
   - The closest value to $$ 50.27 \text{ in}^2 $$ among the given options is $$ 50.24 \text{ in}^2 $$.

**Answer:** $$ 50.24 \mathrm{in.}^{2} $$
The area of the cake's top is approximately $$ 50.24 \text{ in}^2 $$, so $$ 50.24 \mathrm{in.}^{2} $$ of icing is needed.

The decorative icing around the top edge of a circular cake measures
approximately 25.12 inches in length. How much icing is needed to cover the
entire top of the cake?

Upstudy AI Solution

Answer

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