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3 years ago

What is the volume of the prism below?

Mathematics

2 answers:

julia-pushkina [17]3 years ago

6 0

Answer: D. $168\ m^3$

Step-by-step explanation:

We know that the volume of a prism is given by :-

$V=\dfrac{1}{2}*\text{base area*height}$

Now, from the given picture, the dimensions of the base of the prism = $7\ m\times8\ m$

Thus, Base Area = $7\times8=56\ m^2$

Height of prism = 6 m

Therefore, the volume of the prism is given by ;-

$V=\dfrac{1}{2}*56\times6=168\ m^3$

Hence, Volume of the given prism = $168\ m^3$

ASHA 777 [7]3 years ago

5 0

The answer is D. 168 units^3

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Problem 2

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3 years ago

1) Let f(x)=ax2+bx+c for some value of a, b and c. f intersects the x-axis when x=−2 or x=3, and f( 1 3 )=−25. Find the values o

antiseptic1488 [7]

Answer:

1) a = -⅙, b = ⅙, c = 1

2) 6 units

Step-by-step explanation:

1) f(x) = ax² + bx + c

Given the roots, we can write this as:

f(x) = a (x + 2) (x − 3)

We know that f(13) = -25, so we can plug this in to find a:

-25 = a (13 + 2) (13 − 3)

-25 = 150a

a = -⅙

Therefore, the factored form is:

f(x) = -⅙ (x + 2) (x − 3)

Distributing:

f(x) = -⅙ (x² − x − 6)

f(x) = -⅙ x² + ⅙ x + 1

Graph: desmos.com/calculator/6m6tjoodvb

2) Volume of a right prism is area of the base times the height.

V = Ah

The base is an equilateral triangle. Area of a triangle is one half the base times height.

V = ½ ab h

The height of the triangle is the same as the height of the prism.

V = ½ bh²

In an equilateral triangle, the height is equal to half the base times the square root of 3.

V = ½ b (½√3 b)²

V = ⅜ b³

Given that V = 81, solve for b.

81 = ⅜ b³

216 = b³

b = 6

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3 years ago