Question

Cones



Two similar cones are shown in the image below.



What is the approximate surface area of the larger cone?
Answer
978.5 square yards
1,103.1 square yards
1544.4 square yards
2,162.3 square yards

Answer 1

The formula to calculate the surface area of a cone is given by\[SA=\pi rs+\pi r^2\]where r is the radius of the base and s is the slope. We need to know the radius of the larger cone to calculate the surface area of the larger cone. How would you determine that?

Answer 2

Hint: the cones are similar

Answer 3

so the answer to the smaller cone would be 1102.14

Answer 4

You are being asked what the surface area of the larger cone is, not the smaller cone.

Answer 5

yea but you said that we need the surface area of the smaller cone to find the bigger cone..

Answer 6

No, I said we need the radius of the larger cone. How can you find the surface area of the larger cone from the surface area of the smaller? There is a way to do it.

Answer 7

lol, thats what i thought i didn't understand what you said at first. And im not sure how to find the radius of the bigger cone.

Answer 8

Because the cones are similar, that means the ratios of the radii are equal to the ratio of the slopes or\[\frac {r}{42}=\frac{9}{30}\]where r is the radius of the larger cone.

Answer 9

er.. idk how to do it :(

Answer 10

Solve this equation for r.\[\frac {r}{42}=\frac{9}{30}\]Is that what you don't know how to do? I'll give you a hint. Multiply both sides by 42.

Answer 11

Yea idk how to solve for r

Answer 12

Did you try to multiply both sides of the equation by 42?

Answer 13

so it would be: r42/1764 = 378/1260 if i were to multi both sides.

Answer 14

I'm not sure where you got that. \[\cancel {42}\frac {r} {\cancel {42}}=42\frac {9}{30}\] Once you have the value for r, plug it into the formula for the surface area above, remembering that s=42 for the big cone.
I have to go eat dinner, so good luck!

Answer 15

ok ty, enjoy your dinner

Answer 16

sorry to bother.. *sigh* i still dont know what to do with the 42 9/30..

Answer 17

\[r=\cancel {42}7 \frac {9}{\cancel {30}5}=\frac{63} 5=12.6 \] So now, use the equation\[SA=\pi rs+\pi r^2\]where \[r=12.6 \text { yd}\]\[s= 42 \text { yd}\] and \[\pi=3.14\]