Math / Geometry

QuestionUSE YOUR KNOWLEDGE OF CIRCLES TO ANSWER EACH QUESTION BELOW. DRAG THE CORRECT SOLUTION TO THE WHITE BOX. NOT ALL CHOICES WILL BE USED.
1 Brad will put fencing around a circular area in his yard for some baby goats he purchased. If the circular area will have a radius of 10 feet, how many feet of fencing will Brad need? $\square$ ft
3 Kaitlin is choosing between iwo circular wall clocks. One has a radius of 5 inches while the other has a radius of 6 inches. How much more wall space will the clock with a radius of 6 inches cover? $\square$ $\mathrm{in}^{2}$
2 Pam ordered a circular hot tub cover with a diameter of 80 inches. Find the area of the hot tub cover. $\square$ $i n^{2}$
5024 251.2 31.4 34.54
37 18.5 62.8
DRAG THESE

Studdy Solution

STEP 1

1. The problems involve calculations related to circles.
2. The necessary mathematical constants and formulas are known (e.g., $\pi$ ).
3. The solutions provided are to be matched with the correct problem.

STEP 2

1. Calculate the circumference of the circular area for the fencing.
2. Calculate the area of the circular hot tub cover.
3. Calculate the difference in area between the two wall clocks.

STEP 3

Calculate the circumference of the circular area for Brad's fencing using the formula for the circumference of a circle:
$C = 2\pi r$
where $r = 10$ feet.
$C = 2 \times \pi \times 10$
$C \approx 2 \times 3.14 \times 10$
$C \approx 62.8 \text{ ft}$
Match the solution $62.8$ with Brad's fencing problem.

STEP 4

Calculate the area of the circular hot tub cover using the formula for the area of a circle:
$A = \pi r^2$
The diameter is $80$ inches, so the radius $r = \frac{80}{2} = 40$ inches.
$A = \pi \times (40)^2$
$A \approx 3.14 \times 1600$
$A \approx 5024 \text{ in}^2$
Match the solution $5024$ with Pam's hot tub cover problem.

STEP 5

Calculate the difference in area between the two wall clocks.
First, calculate the area of each clock:
For the clock with radius $5$ inches:
$A_1 = \pi \times (5)^2$
$A_1 \approx 3.14 \times 25$
$A_1 \approx 78.5 \text{ in}^2$
For the clock with radius $6$ inches:
$A_2 = \pi \times (6)^2$
$A_2 \approx 3.14 \times 36$
$A_2 \approx 113.04 \text{ in}^2$
Calculate the difference:
$\Delta A = A_2 - A_1$
$\Delta A \approx 113.04 - 78.5$
$\Delta A \approx 34.54 \text{ in}^2$
Match the solution $34.54$ with Kaitlin's clock problem.
The solutions are:
1. Brad's fencing: $\boxed{62.8}$ ft
2. Pam's hot tub cover: $\boxed{5024}$ in $^2$
3. Kaitlin's clock: $\boxed{34.54}$ in $^2$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms