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emmainna [20.7K]
3 years ago
10

A brand new filled jar of salsa is 11 cm tall and a has a radius of 6 cm. Kelly eats some of the salsa and the salsa in the jar

is now 6 cm high. Approximately how much salsa did Kelly eat? Round your final answer to the nearest whole number. 188 cm³ 565 cm³ 679 cm³ 1244 cm³
Mathematics
1 answer:
Otrada [13]3 years ago
6 0

Answer:

565cm³

Step-by-step explanation:

If Kelly eats the salsa until it is 6cm high, then she ate, in height, 11cm-6cm=5cm of salsa. The volume of the salsa she ate is in the shape of a cylinder, and the formula for calculating the volume of a cylinder is πr^2h. Since we have the values for r (radius) and h (height), we can solve for the volume.

V=πr^2h

V=π(6cm)^2(5cm)

V=180πcm³

This is equal to about 565cm³.

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Y = height
x = distance from tower

tan(19.9) = y/x

tan(21.8) = y/(x-50)   ( x is 50 feet closer so subtract 50 from x)

find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400

replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)

rewrite to solve for height:
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0.400(x-50) = y  distribute the 0.400 and rewrite as 0.400x-20 =y

now solve:

0.362x = 0.400x-20

add 20 to each side:
0.362x +20 = 0.400x

subtract 0.362x from each side:

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divide both sides by 0.038
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now that x is known replace x in the original equation and solve for y:

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0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5

the height of the tower is 190.5 feet
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