91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 12, Problem 20RP

To determine

To calculate: The volume and total surface area of right cylindrical piece.

Expert Solution & Answer

Answer to Problem 20RP

The volume is $271.5$ and total surface area is $632.25$ .

Explanation of Solution

Given information:

A rectangle with dimensions 10 and 30. Measure of arc is $60∘$ .

Formula used:

Area of equilateral triangle: $A=s243$

s = side of equilateral triangle Area of sector $=(measure of arc360o)πr2$

r = radius of circle

Area of rectangle: $A=l×w$

l = length of rectangle

w= width of rectangle Area of cylinder $=C×h$

C = Circumference of cylinder and h = height of cylinder

Volume of prism $=B×h$

B = Base area of prism and h = height of prism

Calculation:

Geometry For Enjoyment And Challenge, Chapter 12, Problem 20RP

To find B , find the area of the shaded segment. The inscribed triangle will be equilateral, so the radii will be 10 because all sides of an equilateral triangles are congruent.

$Asector=(measure of arc360o)πr2=(60o360o)π(10)2=16×100π=503π$

$AEquilateral triangle=s243AEquilateral triangle=(10)243AEquilateral triangle=10043AEquilateral triangle=253B=Asector-AEquilateral triangle=503π−253=52.35−43.30=9.05$

Area of rectangle $=l×w=10×30=300$

Lateral area of cylinder $=C×h$

$C=2πr=2π×10=20πh=30$

Lateral area of cylinder $=20π×30=600π=1884.95$

Total Area = 2B + Area of rectangle + $(measure of arc360o)×$ Lateral area of cylinder

Total Area $=(2(9.05))+300+((60∘360∘)×1884.95)$

Total Area $=18.1+300+314.15$

Total Area $=632.25$

Volume of prism $=B×h$

$B=9.05,h=30.$

Volume of prism $=9.05×30$

Volume of prism $=271.5$

Chapter 12, Problem 19RP

Chapter 12, Problem 21RP

Chapter 12 Solutions

Geometry For Enjoyment And Challenge

Ch. 12.1 - Prob. 1PSA Ch. 12.1 - Prob. 2PSA Ch. 12.1 - Prob. 3PSA Ch. 12.1 - Prob. 4PSA Ch. 12.1 - Prob. 5PSA Ch. 12.1 - Prob. 6PSB Ch. 12.1 - Prob. 7PSB Ch. 12.1 - Prob. 8PSB Ch. 12.1 - Prob. 9PSC Ch. 12.1 - Prob. 10PSC

Ch. 12.1 - Prob. 11PSC Ch. 12.2 - Prob. 1PSA Ch. 12.2 - Prob. 2PSA Ch. 12.2 - Prob. 3PSA Ch. 12.2 - Prob. 4PSA Ch. 12.2 - Prob. 5PSA Ch. 12.2 - Prob. 6PSB Ch. 12.2 - Prob. 7PSB Ch. 12.2 - Prob. 8PSB Ch. 12.2 - Prob. 9PSB Ch. 12.2 - Prob. 10PSC Ch. 12.2 - Prob. 11PSC Ch. 12.2 - Prob. 12PSC Ch. 12.2 - Prob. 13PSC Ch. 12.3 - Prob. 1PSA Ch. 12.3 - Prob. 2PSA Ch. 12.3 - Prob. 3PSA Ch. 12.3 - Prob. 4PSA Ch. 12.3 - Prob. 5PSA Ch. 12.3 - Prob. 6PSB Ch. 12.3 - Prob. 7PSB Ch. 12.3 - Prob. 8PSB Ch. 12.3 - Prob. 9PSB Ch. 12.3 - Prob. 10PSB Ch. 12.3 - Prob. 11PSB Ch. 12.3 - Prob. 12PSC Ch. 12.3 - Prob. 13PSC Ch. 12.3 - Prob. 14PSC Ch. 12.4 - Prob. 1PSA Ch. 12.4 - Prob. 2PSA Ch. 12.4 - Prob. 3PSA Ch. 12.4 - Prob. 4PSA Ch. 12.4 - Prob. 5PSA Ch. 12.4 - Prob. 6PSA Ch. 12.4 - Prob. 7PSB Ch. 12.4 - Prob. 8PSB Ch. 12.4 - Prob. 9PSB Ch. 12.4 - Prob. 10PSB Ch. 12.4 - Prob. 11PSB Ch. 12.4 - Prob. 12PSB Ch. 12.4 - Prob. 13PSB Ch. 12.4 - Prob. 14PSB Ch. 12.4 - Prob. 15PSB Ch. 12.4 - Prob. 16PSB Ch. 12.4 - Prob. 17PSB Ch. 12.4 - Prob. 18PSB Ch. 12.4 - Prob. 19PSC Ch. 12.4 - Prob. 20PSC Ch. 12.4 - Prob. 21PSC Ch. 12.4 - Prob. 22PSC Ch. 12.5 - Prob. 1PSA Ch. 12.5 - Prob. 2PSA Ch. 12.5 - Prob. 3PSA Ch. 12.5 - Prob. 4PSA Ch. 12.5 - Prob. 5PSA Ch. 12.5 - Prob. 6PSA Ch. 12.5 - Prob. 7PSA Ch. 12.5 - Prob. 8PSB Ch. 12.5 - Prob. 9PSB Ch. 12.5 - Prob. 10PSB Ch. 12.5 - Prob. 11PSB Ch. 12.5 - Prob. 12PSB Ch. 12.5 - Prob. 13PSB Ch. 12.5 - Prob. 14PSB Ch. 12.5 - Prob. 15PSB Ch. 12.5 - Prob. 16PSB Ch. 12.5 - Prob. 17PSC Ch. 12.5 - Prob. 18PSC Ch. 12.5 - Prob. 19PSC Ch. 12.5 - Prob. 20PSC Ch. 12.6 - Prob. 1PSA Ch. 12.6 - Prob. 2PSA Ch. 12.6 - Prob. 3PSA Ch. 12.6 - Prob. 4PSA Ch. 12.6 - Prob. 5PSA Ch. 12.6 - Prob. 6PSB Ch. 12.6 - Prob. 7PSB Ch. 12.6 - Prob. 8PSB Ch. 12.6 - Prob. 9PSB Ch. 12.6 - Prob. 10PSB Ch. 12.6 - Prob. 11PSB Ch. 12.6 - Prob. 12PSC Ch. 12.6 - Prob. 13PSC Ch. 12.6 - Prob. 14PSC Ch. 12.6 - Prob. 15PSC Ch. 12.6 - Prob. 16PSC Ch. 12.6 - Prob. 17PSD Ch. 12.6 - Prob. 18PSD Ch. 12 - Prob. 1RP Ch. 12 - Prob. 2RP Ch. 12 - Prob. 3RP Ch. 12 - Prob. 4RP Ch. 12 - Prob. 5RP Ch. 12 - Prob. 6RP Ch. 12 - Prob. 7RP Ch. 12 - Prob. 8RP Ch. 12 - Prob. 9RP Ch. 12 - Prob. 10RP Ch. 12 - Prob. 11RP Ch. 12 - Prob. 12RP Ch. 12 - Prob. 13RP Ch. 12 - Prob. 14RP Ch. 12 - Prob. 15RP Ch. 12 - Prob. 16RP Ch. 12 - Prob. 17RP Ch. 12 - Prob. 18RP Ch. 12 - Prob. 19RP Ch. 12 - Prob. 20RP Ch. 12 - Prob. 21RP Ch. 12 - Prob. 22RP Ch. 12 - Prob. 1CR Ch. 12 - Prob. 2CR Ch. 12 - Prob. 3CR Ch. 12 - Prob. 4CR Ch. 12 - Prob. 5CR Ch. 12 - Prob. 6CR Ch. 12 - Prob. 7CR Ch. 12 - Prob. 8CR Ch. 12 - Prob. 9CR Ch. 12 - Prob. 10CR Ch. 12 - Prob. 11CR Ch. 12 - Prob. 12CR Ch. 12 - Prob. 13CR Ch. 12 - Prob. 14CR Ch. 12 - Prob. 15CR Ch. 12 - Prob. 16CR Ch. 12 - Prob. 17CR Ch. 12 - Prob. 18CR Ch. 12 - Prob. 19CR Ch. 12 - Prob. 20CR Ch. 12 - Prob. 21CR Ch. 12 - Prob. 22CR Ch. 12 - Prob. 23CR Ch. 12 - Prob. 24CR Ch. 12 - Prob. 25CR Ch. 12 - Prob. 26CR Ch. 12 - Prob. 27CR Ch. 12 - Prob. 28CR Ch. 12 - Prob. 29CR Ch. 12 - Prob. 30CR Ch. 12 - Prob. 31CR Ch. 12 - Prob. 32CR Ch. 12 - Prob. 33CR Ch. 12 - Prob. 34CR Ch. 12 - Prob. 35CR Ch. 12 - Prob. 36CR Ch. 12 - Prob. 37CR Ch. 12 - Prob. 38CR Ch. 12 - Prob. 39CR Ch. 12 - Prob. 40CR Ch. 12 - Prob. 41CR Ch. 12 - Prob. 42CR

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