The answer is c because power of two is multiplying it by itself
6+5+x=41
11+x=41
11+-11+x=41+-11
x=30
Sue is 30 years old
A) Yes, the smaller cone is similar to the original cone. They are similar because the smaller cone is half of the original cone.
B) The volume of the larger cone is 56.52 and the volume for the smaller cone is 7.065
![V=3.14* 3^2\frac{6}{3}](https://tex.z-dn.net/?f=V%3D3.14%2A%203%5E2%5Cfrac%7B6%7D%7B3%7D)
![V=3.14*1.5^2\frac{3}{3}\\](https://tex.z-dn.net/?f=V%3D3.14%2A1.5%5E2%5Cfrac%7B3%7D%7B3%7D%5C%5C)
C) The ratio of the volume of the larger cone and the smaller cone is the top/smaller cone is half the volume of the bottom/larger cone
D) The Volume of the frustum is 49.455
![V = (1/3) * 3.14 * 3* (1.5^2 + 3^2 + (1.5 * 3))](https://tex.z-dn.net/?f=V%20%3D%20%281%2F3%29%20%2A%203.14%20%2A%203%2A%20%281.5%5E2%20%2B%203%5E2%20%2B%20%281.5%20%2A%203%29%29)
Answer:
a. ![30.36\ cm^2](https://tex.z-dn.net/?f=30.36%5C%20cm%5E2)
b. ![1.6\ cm](https://tex.z-dn.net/?f=1.6%5C%20cm)
Step-by-step explanation:
a. You know that the dimensions of Rectangle A are ![2\ cm* 3\frac{1}{5}\ cm=2\ cm* 3.2 cm](https://tex.z-dn.net/?f=2%5C%20cm%2A%203%5Cfrac%7B1%7D%7B5%7D%5C%20cm%3D2%5C%20cm%2A%203.2%20cm)
Since Rectangle B’s dimensions are
(which is 0.6 cm) larger than Rectangle A’s dimensions, then the dimensions of Rectangle B are:
![(2\ cm+0.6\ cm)( 3.2\ cm+0.6\ cm)=2.6\ cm*3.8\ cm](https://tex.z-dn.net/?f=%282%5C%20cm%2B0.6%5C%20cm%29%28%203.2%5C%20cm%2B0.6%5C%20cm%29%3D2.6%5C%20cm%2A3.8%5C%20cm)
Since Rectangle C’s dimensions are
(which is 0.6 cm) larger than Rectangle B's dimensions, then the dimensions of Rectangle C are:
![(2.6\ cm+0.6\ cm)( 3.8\ cm+0.6\ cm)=3.2\ cm*4.4\ cm](https://tex.z-dn.net/?f=%282.6%5C%20cm%2B0.6%5C%20cm%29%28%203.8%5C%20cm%2B0.6%5C%20cm%29%3D3.2%5C%20cm%2A4.4%5C%20cm)
The find the total area of all three rectangles you must add the products obtained when you multiply their dimensions. Then:
![A_t=(2\ cm* 3.2 cm)+(2.6\ cm*3.8\ cm)+(3.2\ cm*4.4\ cm)\\\\A_t=30.36\ cm^2](https://tex.z-dn.net/?f=A_t%3D%282%5C%20cm%2A%203.2%20cm%29%2B%282.6%5C%20cm%2A3.8%5C%20cm%29%2B%283.2%5C%20cm%2A4.4%5C%20cm%29%5C%5C%5C%5CA_t%3D30.36%5C%20cm%5E2)
b. The perimeter of a rectangle can be calculated with this formula:
![P=2l+2w](https://tex.z-dn.net/?f=P%3D2l%2B2w)
Where "l" is the lenght and "w" is the width.
Knowing the dimensions of each rectangleg, you can calculate the total perimeter as follows:
![P_t=(2)[(2\ cm+ 3.2 cm)+(2.6\ cm+3.8\ cm)+(3.2\ cm+4.4\ cm)]\\\\P_t=38.4\ cm](https://tex.z-dn.net/?f=P_t%3D%282%29%5B%282%5C%20cm%2B%203.2%20cm%29%2B%282.6%5C%20cm%2B3.8%5C%20cm%29%2B%283.2%5C%20cm%2B4.4%5C%20cm%29%5D%5C%5C%5C%5CP_t%3D38.4%5C%20cm)
Then, if a 40-cm coil of wire was used to form the rectangles, the amount of wire that is left is:
![40\ cm-38.4\ cm=1.6\ cm](https://tex.z-dn.net/?f=40%5C%20cm-38.4%5C%20cm%3D1.6%5C%20cm)