Answer:
(a)205
(b)5 Packages
Step-by-step explanation:
Therefore:
Therefore, Volume of the lemonade Monica Started with is
The diameter of the cup =8cm
Therefore, Radius =8/2 =4cm
Height of the Cup =11cm
Volume of a Cone=
The number of cups needed to empty the 10 gallon cooler =37850÷184.31
=205.36
Cups
(b)If the Cups are sold in packages of 50
Number of Package to be bought =205 ÷ 50 =4.1
She would need to buy 5 packages.
According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
Also,
and
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
To learn more about similarity of triangles, refer to this link:
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