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3 years ago

9

Pilar wanted to use estimation to solve a decimal addition problem. She correctly used estimation to rewrite the problem as 12 +

3 + 5 + 6. What could her original problem have been?
12.38 + 4.45 + 4.14 + 6.7
12.5 + 3.05 + 5.23 + 0.6
11.5011 + 3.6 + 5.17 + 5.7
11.75 + 3.299 + 5.31 + 6.27

Advanced Placement (AP)

2 answers:

alekssr [168]3 years ago

7 0

Answer:

B

Explanation:

Paraphin [41]3 years ago

4 0

Answer:

B!

Explanation:

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Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.

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Answer:

$r = 5.24$ --- Radius

$h = 10.48$ --- Height

Explanation:

Given

Object: Can (Cylinder)

$Surface\ Area = 517.8cm^2$

Required

Maximize the volume

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$S.A = 2\pi r^2 + 2\pi rh$

Substitute 517.8 for S.A

$517.8 = 2\pi r^2 + 2\pi rh$

Divide through by 2

$258.9 = \pi r^2 + \pi rh$

Factorize:

$258.9 = \pi r(r + h)$

Divide through by $\pi r$

$\frac{258.9}{\pi r} = r + h$

Make h the subject

$h = \frac{258.9}{\pi r} - r$ --- (1)

Volume (V) is calculated as:

$V = \pi r^2h$

Substitute (1) for h

$V = \pi r^2(\frac{258.9}{\pi r} - r)$

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$V = 258.9r - \pi r^3$

Differentiate V

$V' = 258.9 - 3\pi r^2$

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$0 = 258.9 - 3\pi r^2$

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$3\pi r^2 = 258.9$

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Divide through by $\pi$

$r^2 = \frac{86.3}{\pi}$

$r^2 = \frac{86.3*7}{22}$

$r^2 = \frac{604.1}{22}$

Take square root of both sides

$r = \sqrt{\frac{604.1}{22}$

$r = 5.24$

Recall that:

$h = \frac{258.9}{\pi r} - r$

Substitute 5.24 for r

$h = \frac{258.9}{\pi * 5.24} - 5.24$

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$h = 15.72 - 5.24$

$h = 10.48$

Hence, the dimension that maximize the volume is:

$r = 5.24$ --- Radius

$h = 10.48$ --- Height

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