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WARRIOR [948]
3 years ago
8

this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm

Mathematics
1 answer:
scoundrel [369]3 years ago
6 0

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

\frac{b}{H-h}=\frac{B}{H}\\  b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm

The volume of the frustrum is given by:

V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3

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100-0.0124=99.9876

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divide both sides by P
1/10=0.999876^t
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divide both sides by (ln(0.999876))
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5 0
2 years ago
5. If the tree's circumference is 141.3ft, what is its diameter?
BigorU [14]

Answer:

d ≈ 45 ft

General Formulas and Concepts:

<u>Symbols</u>

  • π (pi) ≈ 3.14

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Geometry</u>

  • Circumference of a Circle Formula: C = πd

Step-by-step explanation:

<u>Step 1: Define</u>

Circumference <em>C </em>= 141.3 ft

<u>Step 2: Solve for </u><em><u>d</u></em>

  1. Substitute in <em>C</em> [Circumference Formula]:                                                       141.3 ft = πd
  2. Substitute in π (approximation):                                                                      141.3 ft ≈ 3.14d
  3. [Division Property of Equality] Divide both sides by 3.14:                              45 ft ≈ d
  4. Rewrite:                                                                                                             d ≈ 45 ft
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