Question

METAL!!!!!!!
What is the surface area of a conical grain storage tank that has a height of 37 meters and a diameter of 16 meters? Round the answer to the nearest square meter.
A. 2,831 square meters
B. 2,664 square meters
C. 1,152 square meters
D. 1,131 square meters
@jim_thompson5910

Answer 1

Refer to this equation to find the surface area of a cone

Answer 2

height is 37 and diameter is 8

Answer 3

The diameter is 16, what is the radius?

Answer 4

i mean the radius is 8

Answer 5

\[SA = \pi r^{2} + \pi r l\]
You will need to solve for l, the lateral height.

r, h, and l make a special shape. How can you use the relationship between r, h, and l to solve for l?

Answer 6

okay so I multiply 37x8?

Answer 7

Not quite; what shape do r, h, and l form?

Answer 8

cone

Answer 9

On a 3-dimensional perspective, yes absolutely.

However, h, r, and l form a right triangle looking from the 2D perspective.

You can use the Pythagorean Theorem to solve for l given r and h.

Answer 10

oh ok

Answer 11

Solve for l :)

Then use the Surface Area equation

Answer 12

Insight:
A cone is basically formed by rotating the triangle 360 degrees, hence why pi is involved.

Answer 13

ok so how do i solve for l?

Answer 14

Pythagorean Theorem, your two legs will be h and r. Your hypotenuse will be l.

\[a^{2} + b^{2} = c^{2}\] so
\[r^{2} + h^{2} = l^{2}\]
You already have values for r and h, so solve for l.

Answer 15

8^2+37^2=L
IS THAT RIGHT

Answer 16

yes :)

Answer 17

well acttually no

Answer 18

You need to square L as well

Answer 19

64+1369=L^2

Answer 20

yes, so take the square root of both sides to get L

Answer 21

\[64 + 1369 = L^{2}\]
\[1433 = L^{2}\]
\[L = \sqrt{1433}\]

Answer 22

ok so l=1433

Answer 23

L is the square root of 1433

Answer 24

37.8

Answer 25

This is what you have now:
\[r = 8, h = 37, l = \sqrt{1433}\]

Answer 26

right. So now you use the surface area equation

Answer 27

\[SA = \pi r^{2} + \pi r l\]

Answer 28

25.12 for the first part

Answer 29

Try to leave everything in terms of pi in your calculator, and approximate at the end

Answer 30

wait what...

Answer 31

\[SA = \pi (8)^{2} + \pi (8)(\sqrt{1433})\]
\[SA = 64\pi + 8\pi(\sqrt{1433})\]

Answer 32

You should use a calculator and multiply/add those values to get your surface area

Answer 33

200.96+8pi(37.8

Answer 34

200.96+25.12(37.8)

Answer 35

Yes, that's the right idea.

The reason you should use the pi key on your calculator is to get a closer answer:
\[SA = \pi (8)^{2} + \pi (8)(\sqrt{1433}) \approx 1152.461509 \]
So answer choice D. 1152 square meters