Mathematics, 06.06.2020 23:02 mari8493

45 POINTS FOR SOLVING THIS!!

Answers: 1

Show answers

Answers

Answer from: jade5801

157.98 in^2

Step-by-step explanation:

Given: volume of pyramid is equal to 100 cubic inches and height of the pyramid is 5 inches

To find: surface area of the pyramid

Solution:

Let h denotes the height of the pyramid and 'a' denotes side of the square base of the pyramid.

Volume of the pyramid = $\frac{1}{3}a^2h$

Also,

Volume of the pyramid = 100 cubic inches

$\frac{1}{3}a^2h=100\\\frac{1}{3}a^2(5)=100\\a^2=\frac{100\times 3}{5}=60\\a=\sqrt{60}$

Surface area of the pyramid $(S) =a\sqrt{4h^2+a^2}+a^2$

So,

$S=\sqrt{60}\sqrt{100+60}+60\\=\sqrt{60}\sqrt{160}+60\\=\sqrt{9600}+60\\=97.9796+60\\=157.9796\\\approx 157.98$

Surface area = 157.98 in^2

Answer from: FailingstudentXD

Surface area of the pyramid = 157.99 in²

Step-by-step explanation:

Volume of a pyramid is given by the formula,

Volume = $\frac{1}{3}(\text{Area of the base})\times \text{height}$

100 = $\frac{1}{3}\text{(Side)}^{2} \times \text{height}$

300 = s² × 5

s² = 60

s = √60

s = 2√15 in ≈ 7.746 in

Now surface area of the pyramid = Area of base + 4×(Area of one lateral side)

Area of square base = (Side)² = 60 in

Area of one lateral side = $\frac{1}{2}(\text{Base})(\text{Lateral height})$

Since Lateral height = $\sqrt{(h)^{2}+(\frac{S}{2})^{2}}$ [By applying Pythagoras theorem in the given triangle]

= $\sqrt{(5)^{2}+(3.873)^{2}}$

= $\sqrt{25+15}$

= $\sqrt{40}$

= 6.325 in.

Now area of lateral side = $\frac{1}{2}(7.746)(6.325)$

= 24.497 in²

Surface area of the pyramid = 60 + (4×24.497)

= 60 + 97.987

= 157.987 in²

≈ 157.99 in²

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

The answer to your question is b’(16,14)

Another question on Mathematics

Mathematics, 21.06.2019 23:30

Arational number that is equivalent to -20/4?

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

On ryan's last social studies test there were two types of questions true/false worth 3 points each and multiple choice questions worth 4 points each

Answers: 3

Answer

Mathematics, 22.06.2019 02:00

Look at this system of equations. -3x + 3y = 12 y = x + 4 the solution set of this system is best explained by which of these statements? a) the graphs of the equations are the same line because the equations have the same slope and the same y-intercept. the system has infinitely many solutions. b) the graphs of the equations are parallel lines because they have the same slope but different y-intercepts. the system has no solution. c) the graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. the system has exactly one solution. d) the graphs of the equations are lines that intersect at one point because the equations have the same slope and the same y-intercept. the system has exactly one solution.

Answers: 2

Answer

Mathematics, 22.06.2019 04:30

Ana’s dachshund weighed 5 5/8 pounds when it was born . by age 4 the dog weighed 6 times as much. fill each box with a number or symbols from the list to show how to find the weight of ana’s dog at age 4 . not all numbers and symbols my be used

Answers: 2

Answer

You know the right answer?

45 POINTS FOR SOLVING THIS!!
...

Questions