All categories

3 years ago

The two pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.

Mathematics

1 answer:

mihalych1998 [28]3 years ago

5 0

Answer:

A) 5.12mm³

Step-by-step explanation:

Step 1

Find the volume of the bigger pyramid

This is a triangular based pyramid.

The formula to use is given as Volume of Pyramid =

1/3 × Area of the triangle × Height

Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²

Volume of the large pyramid = 1/3 × 6mm² × 5mm

= 10mm³

We are given the length of the small pyramid as 4mm

We would be using was is known as scale factor to find the volume of the small pyramid

The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³

k = 4³/5³

k = Volume of small pyramid/ Volume of large pyramid

Volume of small pyramid = X

Volume of large pyramid = 10mm³

Hence,

4³/5³ = X/10

Cross Multiply

= 4³ × 10 = 5³ × X

X = (4³ × 10)/ 5³

X = 5.12mm³

You might be interested in

The volume of a cylinder is 8,478 cubic inches, and the radius is 15 inches. Which measurement is closest to the

MrRa [10]

I think it might be 90in. I’m not quite sure

5 0

2 years ago

Read 2 more answers

PLZ HELP ME THANKS. If 3x-5-6x-2 is equaled to -1. Then how do I "check it"?

Nezavi [6.7K]

Answer:

3(-1)-5-6(-1)-2. You found the value of X, so you need to put it back into the equation to see if it equals out.

5 0

3 years ago

Read 2 more answers

What is the answer to m+14=18-m?

Ganezh [65]

Step-by-step explanation:

m=2

.................

7 0

2 years ago

Read 2 more answers

Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

2 years ago

Who's good at math? i need help ASAP. *don't mind the red numbers, i think they're wrong*

shepuryov [24]

Answer:

Seems like someone answered them, because the red writing is right, but here's the answers with explanation

Step-by-step explanation:

The vertex is the point at which the graph changes direction as we go from left to right.
Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
Now the answers:

Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so minimum
vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so minimum
vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is maximum
Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is maximum
vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is minimum
vertex is (0.5,5) because it was getting big then changed and started getting smaller so maximum

8 0

3 years ago