Question

8. A DVD has a diameter of 12 centimeters. What is the area of the DVD? Round
your answer to the nearest hundredth.
9. A company makes steel lids that have a diameter of 13 inches. What is the
area of each lid? Round your answer to the nearest hundredth.
10. A circular garden has an area of 64 square yards. What is the circumference
of the garden? Give your answer in terms of .
11. Reasoning A small silver dollar pancake served at a restuarant has a circumference
of 27 inches. A regular pancake has a circumference of 4 inches. Is the area of the
regular pancake twice the area of the silver dollar pancake? Explain.​

Answer 1

Answer:

Part 8) The area of DVD is 113.04 square centimeters

Part 9) The area of each lid is 132.67 square inches

Part 10) The circumference of the garden is $16\pi\ yards$

Part 11) No, the area of the regular pancake is 4 times the area of the small pancake

Step-by-step explanation:

Part 8) we know that

The area of the circle is given by the formula

$A=\pi r^{2}$

where

r is the radius

we have

$r=12/2=6\ cm$ ---> the radius is half the diameter

assume

$\pi =3.14$

substitute

$A=(3.14)(6)^{2}=113.04\ cm^2$

Part 9) we know that

The area of the circle is given by the formula

$A=\pi r^{2}$

where

r is the radius

we have

$r=13/2=6.5\ in$ ---> the radius is half the diameter

assume

$\pi =3.14$

substitute

$A=(3.14)(6.5)^{2}=132.67\ in^2$

Part 10)

step 1

we know that

The area of the circle is given by the formula

$A=\pi r^{2}$

where

r is the radius

we have

$A=64\pi \ yd^2$

substitute

$64\pi=\pi r^{2}$

solve for r

simplify and take square root both sides

$r=8\ yd$

step 2

Find the circumference of the garden

we know that

The circumference of the circle is given by

$C=2\pi r$

we have

$r=8\ yd$

substitute

$C=2\pi (8)$

$C=16\pi\ yd$

Part 11)

The correct question is

A small silver dollar pancake served at a restaurant has a circumference

of 2 inches. A regular pancake has a circumference of 4 inches. Is the area of the  regular pancake twice the area of the silver dollar pancake?

step 1

Find the scale factor

we know that

All circles are similar

so

The ratio of its circumferences is equal to the scale factor

Let

z ----> the scale factor

x ---> circumference of the regular pancake

y ----> circumference of the small silver dollar pancake

so

$z=\frac{x}{y}$

substitute the given values

$z=\frac{4}{2}=2$

step 2

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ---> area of the regular pancake

y ----> area of the small silver dollar pancake

so

$z^{2}=\frac{x}{y}$

we have

$z=2$

substitute

$2^{2}=\frac{x}{y}$

$4=\frac{x}{y}$

solve for x

$x=4y$

therefore

The area of the regular pancake is 4 times the area of the small pancake