Container a is a cylinder with a radius of 9 units and a height of 9 units. a right cone has been carved from its base and has a height of 9 units. container b has the same radius as container a. which statement derives the formula to find the volume of container b?
a. π(92)(9) − 1 over 3π(92)(9)
b. 2[π(92)(9) − 1 over 3π(92)(9)]
c. 1 over 3π(92)(9) − π(92)(9)
d. 2[1 over 3π(92)(9) − π(92)(9)]

answer:

  a.   π(9^2)(9) - (1/3)(9^2)(9)

step-by-step explanation:

we assume that container a is the whole cylinder, and that container b is the cylinder with the cone carved out.

the formula for the volume of a cylinder is

  vcyl = πr²h

the formula for the volume of a cone is

  vcon = (1/3)πr²h

here, we have r=h=9 in both cases, and we want to find the difference of volumes. filling in the numbers gives

  vcyl - vcon = π(9²)(9) - (1/3)(9²)(9) . . . matches choice a

comment on notation

exponents rarely get copied properly from other applications to so some editing may be required. if you don't use the equation editor or special mathematical symbols, the plain-text form for an exponent is

  (base)^(exponent) . . . the exponent is signified by a caret (^)

note that grouping symbols may be required. if the exponent has an arithmetic operation in it, then it needs parentheses:

  √(x) = x^(1/2)

  (x^a)(x^b) = x^(a+b)

the use of the word "over" to signify a fraction is unnecessary and ambiguous. the forward slash (/) is usually used for that purpose. as with the caret, any numerator or denominator consisting of more than a single number or letter needs parentheses: (1/a) + (1/b) = (a+b)/(ab). even if you know that the denominator is a single number, as in 1/3, it understanding to put the fraction in parentheses so the appropriate interpretation is clear. (see above for examples. many people write 1/x+1 when they mean 1/(x+1), so if you mean (1/x)+1, it is to write it that way--even though that is how it should be interpreted.)

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x