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lisabon 2012 [21]
3 years ago
12

A cylindrical pail that has the base area of 9 pi inches squared and a height of 10 inches. One friend bought a pyramid mold wit

h a square base with edge length of 4 inches and height of 7 inches. The other friend bought a cone with a radius of 2.5 inches and the height of six inches. What is the volume of these three objects?
Mathematics
1 answer:
FromTheMoon [43]3 years ago
3 0

Answer:

  • cylinder — 90π in³
  • pyramid — 37 1/3 in³
  • cone — 12.5π in³

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = Bh . . . . . where B is the base area and h is the height

The volume of a pyramid or cone is given by ...

  V = (1/3)Bh . . . . . where B is the base area and h is the height

The area of a square of side length s is ...

  A = s²

The area of a circle of radius r is ...

  A = πr²

___

Using these formulas, the volumes of these objects are ...

  cylinder: (9π in²)(10 in) = 90π in³

  square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³

  cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid

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Answer: the expression 12f + 24 represents 12 times a quantity, added to 24.


Expplanation.


The <em>expression 12f + 24</em> is an algebraic <em>expression</em>, especifically a first degree binomial; this is, a polynomial of two terms, whose maximum power is 1.


The algebraic expressions are used to <em>represent</em> word statements in mathematical language.


You can analyze each term of the expression and then tell what the total expresssion represents:


  • The first term <em>12f</em>, where f is a variable with degree 1 (the exponent of the variable), <em>represents</em> the multiplication of a quantity (represented by the variable f) by 12.
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Anit [1.1K]
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