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3 years ago

15

In the accompanying diagram, a right circular cone is carved out of a solid foam cylinder and discarded. What is the volume of t

he foam remaining in the cylinder?
A. 150π cubic units
B. 125π cubic units
C. 100π cubic units
D. 50π cubic units

1 answer:

Stolb23 [73]3 years ago

5 0

Answer:

100π cubic units is left

Step-by-step explanation:

πr²h - 1/3πr²h

π(5)²(6) - 1/3π(5)²(6)

150π - 50π = 100π

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The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its

Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

$b = 3 + 2h$

$Area = 22$

Required

Find the length of the base

The area of a triangle is calculated as thus;

$Area = \frac{1}{2} * b * h$

Substitute 22 for Area and 3 + 2h for b

The formula becomes

$22 = \frac{1}{2} * (3 + 2h) * h$

Multiply both sides by 2

$2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h$

$44 = (3 + 2h) * h$

Open the bracket

$44 = 3 * h + 2h * h$

$44 = 3h + 2h^2$

Subtract 44 from both sides

$44 - 44 = 3h + 2h^2 - 44$

$0 = 3h + 2h^2 - 44$

Rearrange

$0 = 2h^2 +3h - 44$

$2h^2 +3h - 44 = 0$

At this point, we have a quadratic equation; which is solved as follows:

$2h^2 +3h - 44 = 0$

$2h^2 + 11h - 8h - 44 = 0$

$h(2h + 11) - 4(2h + 11) = 0$

$(h - 4)(2h + 11) = 0$

Split the above

$(h - 4) = 0\ or\ (2h + 11) = 0$

$h - 4 = 0\ or\ 2h + 11 = 0$

Solve the above linear equations separately

$h - 4 = 0$

Add 4 to both sides

$h - 4 + 4 = 0 + 4$

$h = 0 + 4$

$h = 4$ ---- <em>First value of h</em>

$2h + 11 = 0$

Subtract 11 from both sides

$2h + 11 - 11 = 0 - 11$

$2h = 0 - 11$

$2h = -11$

Divide both sides by 2

$\frac{2h}{2} = -\frac{11}{2}$

$h = -\frac{11}{2}$ <em> ------ Second value of h</em>

Since height can be negative, we'll discard $h = -\frac{11}{2}$

Hence, the usable value of height is $h = 4$

Recall that $b = 3 + 2h$

Substitute 4 for h

$b = 3 + 2(4)$

$b = 3 + 8$

$b = 11$

Hence, the length of the base is 11 meters

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3 years ago

3/7 is reduced to what lowest term?

sweet [91]

It can't be simplified, it is already in its lowest term

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3 years ago

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Robert believes that the lengths 8 in, 13 in, and 20 in will form a triangle. Is he correct?

adell [148]

Answer: I think it’s D

Step-by-step explanation:

it’s because 8^2 + 13^2 equals 233 and when square rooted equals 15.26 not 20 so no.

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3 years ago

I need help with this math problem!!

Vesnalui [34]

In order to find which one is or isn't, you need to solve for the value of 'x'.
2x + 15 = 35
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x = 10

Substitute x =10, into equation. If each side are not the same (i.e. 0=2), then that's the equation that is not equivalent,

Answer is B
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Hope this makes sense.

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slega [8]

Answer:

1. 54 and 9/20 km

2. 80 mm

3. 1.142 mi

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Step-by-step explanation:

Do them all by the butterfly method.

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2 years ago