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lakkis [162]
3 years ago
12

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, th

en its volume is:
A) 36
B) 12sqrt3
C)18sqrt3
D)24sqrt3
E)36sqrt3

The correct answer was E. Hoping someone could explain how that is.
Mathematics
1 answer:
almond37 [142]3 years ago
5 0
Letter E is correct.
Area of equilateral trianlge= (1/2) tiime a^2 square root 3
Equation for the base is = x^2+y^2 =9

at x ,
y= square root (9-x^2)
Side of triangle a= 2y

d times Volume = (1/2)a^2 square root 3 dx

d times V= (square root 3) (9-x^2) dx

V= square root 3 INT (9-x^2) dx
-3V= 2square root INT (9-x^2) dx
0
V= 2 square root 3 ( 9x-x^3/3)

V=2 square root 3 ( 27-9)
V= 36 square root 3

The answer is E.
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Step-by-step explanation:

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3 years ago
I need some help on these 3 questions :)
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The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions

<h3>How to simplify the expressions?</h3>

<u>Factor of the polynomial</u>

The polynomial is given as:

2x^3 + 6x^2 + 6x + 18

Factor out 2

2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)

Factorize

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Factor out x + 3

2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)

Expand

2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)

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<u>The length of the pool</u>

The given parameters are:

Area = 2x^3 - 29x + 12

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The length is calculated as:

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This gives

Length = 2x^2 - 29x + 12/x + 4

Factorize the numerator

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Cancel out x + 4

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The expression is given as:

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Evaluate the quotient

3 + (s - 5)/(s^2 - 5 + 2)

Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)

Read more about algebraic expressions at:

brainly.com/question/2164351

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