Pre-Algebra
Pre-Algebra
1st Edition
ISBN: 9780618800766
Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold
Publisher: Houghton Mifflin-High School
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A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
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A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…
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Chapter 10.5, Problem 17E

(a)

To determine

To compare area of base of new cylinder compare to original cylinder.

(a)

Expert Solution
Check Mark

Answer to Problem 17E

4 : 1

Explanation of Solution

Given Information: For original cylinder = Radius = r in and Height = h in.

For new cylinder = Radius = 2r in and Height = 2h in

Formula Used:

Area of Base= π×(radius)2

Calculation:

Area of Base of new cylinder = π×(radius)2

For new cylinder = Radius = 2r in and Height = 2h in

Area of Base of new cylinder = π×(2r)2

Hence,

Area of Base of new cylinder = 4πr2

Area of Base of original cylinder = π×(radius)2

For original cylinder = Radius = r in and Height = h in

Area of Base of original cylinder = π×(r)2

Hence,

Area of Base of original cylinder = πr2

Hence, Ratio

Area of Base of new cylinder : Area of Base of original cylinder

  4πr2 : πr2

4 : 1

(b)

To determine

To compare circumference of base of new cylinder compare to original cylinder.

(b)

Expert Solution
Check Mark

Answer to Problem 17E

2 : 1

Explanation of Solution

Given Information: For original cylinder = Radius = r in and Height = h in.

For new cylinder = Radius = 2r in and Height = 2h in

Formula Used:

Circumference of Base = 2π×radius + 2×height

Calculation:

Circumference of Base of new cylinder = 2π×radius + 2×height

For new cylinder = Radius = 2r in and Height = 2h in

Circumference of Base of new cylinder = 2π×(2r) + 2×(2h)

Hence,

Circumference of Base of new cylinder = 4πr + 4h = 4(πr+h)

Circumference of Base of original cylinder = 2π×radius + 2×height

For original cylinder = Radius = r in and Height = h in

Circumference of Base of original cylinder = 2πr+ 2h

Hence,

Circumference of Base of original cylinder = 2(πr+h)

Hence, Ratio

Circumference of Base of new cylinder : Circumference of Base of original cylinder

   4(πr+h) :  2(πr+h)

2 : 1

(c)

To determine

To compare surface area of base of new cylinder compare to original cylinder.

(c)

Expert Solution
Check Mark

Answer to Problem 17E

4 : 1

Explanation of Solution

Given Information: For original cylinder = Radius = r in and Height = h in.

For new cylinder = Radius = 2r in and Height = 2h in

Formula Used:

Surface area of Base = 2π×radius (height+radius)

Calculation:

Surface area of Base of new cylinder = 2π×radius (height+radius)

For new cylinder = Radius = 2r in and Height = 2h in

Surface area of Base of new cylinder = 2π×(2r) {(2h)+(2r)}

Hence,

Surface area of Base of new cylinder = 4πr ×2(h+r)

Surface area of Base of new cylinder = 8πr (h+r)

Surface area of Base of original cylinder = 2π×radius (height+radius)

For original cylinder = Radius = r in and Height = h in

Surface area of Base of original cylinder = 2πr(h+r)

Hence, Ratio

Surface area of Base of new cylinder : Surface area of Base of original cylinder

  8πr (h+r):  2πr (h+r)

4 : 1

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Chapter 10.5, Problem 16E
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Chapter 10.5, Problem 19E

Chapter 10 Solutions

Pre-Algebra

Ch. 10.1 - Prob. 1CCh. 10.1 - Prob. 2CCh. 10.1 - Prob. 3CCh. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7E
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