Question

BRAINLIEST AND 20 POINTS ANSWER ASAP PLZ


Anyone have answers for Geometry B Unit 6 Lesson 10 test?? Surface area and volume? 31 questions.. my first question is..
1. use euler’s formula to find the missing number
Vertices-13
Edges-28
Faces-?

A.17 B.16 C.18 D.20

and the last one is

31. Whats the maximum vol. of a square pyramid that can fit inside a cube with a side length of 24 cm?

A.2,304 B.4,608 C.6,912 D.13,824

Answer 1

r = m - v + 2, where r = faces, v = vertices, and m = edges

r = 28 - 13 + 2
r = 15 + 2
r = 17, so the first answer is correct.

7. The surface area of a cone is A = pi*r*sqrt(r^2 + H^2)

A = pi*(7)(sqrt(49 + 1849)
A = pi*(7)(43.57)
A = pi*305 = 959 m^2, so the first answer is correct.

13. The volume of the slab is V = HLW
V = (5 yards)(5 yards)(1/12 yards)
V = 25/12 cubic yards

So it costs $46.00*(25/12) = $95.83 of total concrete. The third answer is correct.

21. First, find the volume of the rectangular prism. V = HLW
V = (15 cm)(5 cm)(7 cm)
V = 525 cm^3

Next, find the volume of the pyramid. V = 1/3(BH), where H is the height of the pyramid and B is the area of the base of the pyramid. Note that B = (15 cm)(5 cm) = 75 cm^2

V = (1/3)(75 cm^2)(13 cm)
V = 325 cm^3

Add the two volumes together, the total volume is 850 cm^3. The fourth answer is correct.

22. The volume of a square pyramid is V = 1/3(S^2)(H), where S is the side length and H is the height.

V = (1/3)(20^2 in^2)(21 in)
V = 2800 in^3

Now that we know the volume of this pyramid, and that both pyramids have equal volume, we plugin our V to the equation for the volume.

2800 = (1/3)(84)(S^2)
2800 = 28S^2
100 = S^2
10 in = S, so we have a side length of 10 in, and the first answer is correct.

Answer 2

The missing number using Euler's formula is: Option A. 17

The maximum volume of a square pyramid is: Option B. 4,608

What is Euler's formula?

"It is a geometrical formula. V − E + F = 2, where V represents number of vertices, E represents number of edges and F represents number of faces."

What is square pyramid?

"Square pyramid is a three dimensional geometrical figure where four triangular sides are associated to square base."

What is cube?

"A cube is a three-dimensional geometric structure with six congruent square face."

Formula for volume of a square pyramid:

$V=\frac{1}{3}a^{2}h$

where $a$ represents the length of square base and $h$ represents the height of the pyramid.

Consider the first question,

number of vertices (V) = 13

number of edges (E) = 28

So, using Euler's formula:

$13-28+F=2$

⇒ $-15+F=2$

⇒ $F=2+15$

⇒ $F=17$

So, the number of faces are 17.

Hence, the correct answer is option A. 17

Consider last question,

the side length of a cube = 24 cm

As the square pyramid fit inside a cube.

⇒ the length of the square base of a pyramid $b$ = 24 cm

and the height of a square pyramid $h$ = 24 cm

So, the volume of a square pyramid is,

$V=\frac{1}{3} a^{2} h$

⇒ $V=\frac{1}{3}$ × $24^{2}$ × $24$

⇒ $V= 4608$ $cm^{3}$

Therefore, the maximum volume of a square pyramid that can fit inside a cube with a side length of 24 cm is $4608$ $cm^{3}$.

And the correct answer is option B. 4,608

Learn more about Euler's formula here,

https://brainly.com/question/22069428

Learn more about volume of a square pyramid here:

https://brainly.com/question/2501401

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