A cylinder is inscribed inside of a square prism so that touches each face of the rectangle or prism. The empty space outside of
the cylinder, but inside of the prism is to be filled with a liquid epoxy. If the cylinder has a circumference of 84.78 cm and the writing either prism is 40 cm tall, how many cubic centimeters of epoxy will be required to completely fill the empty spaces?
1 answer:
To solve take (Volume of Prism) - (Volume of Cylinder) = Epoxy
<span>V=(Area of base)(height)
</span>
Both they Cylinder and prism have a height of 40 inches
we can find the sides of the base of the prism by finding the diameter of the cylinder.
C=πd so 84.78 = πd.
Divide both sides by Pi (3.14)
Half of the diameter is the radius to find the area of the cylinder base. 27/2=13.5
The volume of Prism is found by
27*27*40 = 29160 sq cm
The volume of cylinder is found by
using
= 22890.6
29160 - 22890.6 = 6269.4 cubic centimeters
<span>V=(Area of base)(height)
</span>
Both they Cylinder and prism have a height of 40 inches
we can find the sides of the base of the prism by finding the diameter of the cylinder.
C=πd so 84.78 = πd.
Divide both sides by Pi (3.14)
Half of the diameter is the radius to find the area of the cylinder base. 27/2=13.5
The volume of Prism is found by
27*27*40 = 29160 sq cm
The volume of cylinder is found by
using
29160 - 22890.6 = 6269.4 cubic centimeters
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<u>answer (in words)</u>
FALSE. the coordinate pair (5, 2) is not a solution to the equation . in order to figure out whether or not the statement is true or false, plug the
and
values from the coordinate pair (5, 2) into the given equation,
. if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.
<em>(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)</em>
<u>answer (algebraic/steps for solving)</u>
first, plug in 5 for in the equation
.
⇒
then plug in 2 for .
⇒
now your equation is . all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.
⇒
multiply 3 · 2.
⇒
add 10 + 6.
⇒
16 and 10 are <em>not</em> equal, therefore (5, 2) is not a solution to the equation . in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.
i hope this helps! have a great rest of your day <3