1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
2 years ago
8

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

oras' Theorem thank you)
Mathematics
1 answer:
Sveta_85 [38]2 years ago
8 0

Answer:

\displaystyle V_{ \text{pyramid}}= 64 \:  {cm}^{3}

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s

where B stands for Base area

and P for Base Parimeter

so

\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s

now we need our algebraic skills to figure out s

simplify parentheses:

\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144

reduce fraction:

\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32}  \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144

simplify multiplication:

\displaystyle \: 16s + 64 = 144

cancel 64 from both sides;

\displaystyle \: 16s = 80

divide both sides by 16:

\displaystyle \: \therefore \: s = 5

now we'll use Pythagoras theorem to figure out height

according to the theorem

\displaystyle \:  {h}^{2}  +  (\frac{l}{2} {)}^{2}  =  {s}^{2}

substitute the value of l and s:

\displaystyle \:  {h}^{2}  +  (\frac{8}{2} {)}^{2}  =  {5}^{2}

simplify parentheses:

\displaystyle \:  {h}^{2}  +  (4 {)}^{2}  =  {5}^{2}

simplify squares:

\displaystyle \:  {h}^{2}  +  16  =  25

cancel 16 from both sides:

\displaystyle \:  {h}^{2}   =  9

square root both sides:

\displaystyle \:   \therefore \: {h}^{}   =  3

recall the formula of a square pyramid

\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h

where A stands for Base area (l²)

substitute the value of h and l:

\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times  \{8 \times 8 \}\times 3

simplify multiplication:

\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times  64\times 3

reduce fraction:

\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times  64\times \cancel{ \:  3}

hence,

\sf\displaystyle V_{ \text{pyramid}}= 64 \:  {cm}^{3}

You might be interested in
‼️ What is the height of a right triangle with an angle that measures 60 degrees and a base of 14 adjacent to the 60 degree angl
puteri [66]

You'd use tangent for this.

opposite / adjacent

tan 60* = x/14

multiply both sides by 14

tan 60* = 1.73

tan 60* (1.73 x 14) = x

24.22 = x

Your answer should be 24.22


7 0
3 years ago
Math grades assignment unit test part 2 adding and subtracting rational numbers?
Katena32 [7]

Answer: When we add or subtract rational numbers that have the same denominator, we add or subtract only the numerators. The denominators stay the same. When we add or subtract rational numbers with unlike denominators, we need to change the rational numbers to equivalent rational numbers that have the same denominators, before we find the sum or difference. Adding & Subtraction Rational Numbers

Step-by-step explanation:

3 0
2 years ago
13(x - 3)=39 what is answer
artcher [175]
X = 6 after distributing then adding 39 to both sides and then divide by 13

8 0
3 years ago
Read 2 more answers
Mr. Allway’s math class surveyed all the seventh-grade students to find out their favorite sport. The following circle graph sho
JulijaS [17]

Answer:

101 is the answer of the question

3 0
3 years ago
Read 2 more answers
Factorize: Challenge problem:<br> x^2+19x+78<br> help :)
Trava [24]

Answer:

(x + 6)(x + 13)

Step-by-step explanation:

Given

x² + 19x + 78

Consider the factors of the constant term (+ 78) whuch sum to give the coefficient of the x- term (+ 19)

The factors are + 6 and + 13 , since

6 ×13 = + 78 and 6 + 13 = + 19 , then

x² + 19x + 78 = (x + 6)(x + 13) ← in factored form

3 0
2 years ago
Read 2 more answers
Other questions:
  • Simplify each expression. Use positive exponents.
    6·2 answers
  • What is 56/74 in simplest form?
    10·1 answer
  • #7 what is the image of (6,-2) under the translation.
    13·1 answer
  • What are the factors for 51
    9·1 answer
  • What is the midpoint segment with endpoints j(-3,-2),K(4,-6)?
    11·1 answer
  • What is 1/8 x 3/4 iready
    6·2 answers
  • A) If 2 points on the rectangle are (a, b) and (c, d), then identify the two missing points on the rectangle?
    5·1 answer
  • What are the variables and units?
    13·1 answer
  • URGENT A measure of the spacing between atoms is: density inertia mass volume
    11·1 answer
  • (x+2) (x+1)=0
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!