Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?

The root beer mug

Step-by-step explanation:

To known what vessels holds more root beer, we must find the volume (this is the holding capacity) of the two vessels. From the description given, the mug is a cylinder while the glass is a cone.

The volume V of a cylinder whose height is h and radius r may be found as

V = πr²h

The volume V of a cone with similar features

V  = 1/3πr²h

Hence the volume of the mug shaped basically like a cylinder that is eight inches tall with a radius of three inches

=  π * 3² * 8

= 72π Inches³

Given that the cone shaped bottle has a diameter of four inches, the radius r = 4/2

= 2 inches

Hence the volume of the bottle

= 1/3 * π * 2² * 18

= 24π Inches³

Based on comparison, the mug holds more root beer

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²