Answer 259 m 2 Explanation Given Information: Cylinder Height h = 5 m, Cone Diameter d = 7 m., Slant Height l = 6.5 m. and π = 22 7 Formula Used: Surface area of solid = Lateral Surface area of Cone + Surface area of Cylinder Lateral Surface area of Cone = π r l , Surface area of Cylinder = 2 π r ( h + r ) , Radius = D i a m e t e r 2 Calculation: Lateral Surface area of Cone Diameter d = 7 m., Slant Height l = 6.5 m. and π = 22 7 First find Radius r. Hence, Radius = D i a m e t e r 2 Put the value of diameter to find radius of Cone So, Radius = 7 2 m Lateral Surface area of Cone = π r l Radius r = 7 2 m., Slant Height l = 6.5 m. and π = 22 7 Now put the value of r, s and π to find Lateral Surface area of Cone Lateral Surface area of Cone = 22 7 × 7 2 × 6.5 m 2 Hence, Lateral Surface area of Cone = 71.5 m 2 Surface Area of Cylinder- Diameter d = 7 m., Height h = 5 m. and π = 22 7 First find Radius r. Hence, Radius = D i a m e t e r 2 Put the value of diameter to find radius of Cone So, Radius = 7 2 m Surface area of Cylinder = 2 π r ( h + r ) Radius r = 7 2 m., Height h = 5 m. and π = 22 7 Now put the value of r, h and π to find Surface area of Cylinder Surface area of Cylinder = 2 × 22 7 × 7 2 × ( 5 + 7 2 ) m 2 So, Surface area of Cylinder = 22 × 17 2 m 2 Hence, Surface area of Cylinder = 187 m 2 Surface Area of Solid- Surface Area of Solid = Lateral Surface area of Cone + Surface area of Cylinder Now put value of Lateral Surface area of Cone and Surface area of Cylinder Surface Area of Solid = 71.5 m 2 + 187 m 2 Surface Area of Solid = 258.5 m 2 Nearest Surface Area of Solid = 259 m 2

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN: 9780547587776

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

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Concept explainers

Cylinders

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.

Cones

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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Question

Chapter 10.6, Problem 31E

To determine

To calculate the lateral surface area of cone.

Expert Solution & Answer

Answer to Problem 31E

259 m²

Explanation of Solution

Given Information: Cylinder Height h = 5 m, Cone Diameter d = 7 m., Slant Height l = 6.5 m. and π=227

Formula Used:

Surface area of solid = Lateral Surface area of Cone + Surface area of Cylinder

Lateral Surface area of Cone = πrl , Surface area of Cylinder = 2πr(h+r) , Radius = Diameter2

Calculation:

Lateral Surface area of Cone Diameter d = 7 m., Slant Height l = 6.5 m. and π=227

First find Radius r.

Hence,

Radius = Diameter2

Put the value of diameter to find radius of Cone

So, Radius = 72 m

Lateral Surface area of Cone = πrl

Radius r = 72 m., Slant Height l = 6.5 m. and π=227

Now put the value of r, s and π to find Lateral Surface area of Cone

Lateral Surface area of Cone = 227×72×6.5 m²

Hence,

Lateral Surface area of Cone = 71.5 m²

Surface Area of Cylinder- Diameter d = 7 m., Height h = 5 m. and π=227

First find Radius r.

Hence,

Radius = Diameter2

Put the value of diameter to find radius of Cone

So, Radius = 72 m

Surface area of Cylinder = 2πr(h+r)

Radius r = 72 m., Height h = 5 m. and π=227

Now put the value of r, h and π to find Surface area of Cylinder

Surface area of Cylinder = 2×227×72×(5+72) m²

So,

Surface area of Cylinder = 22×172 m²

Hence,

Surface area of Cylinder = 187 m²

Surface Area of Solid-

Surface Area of Solid = Lateral Surface area of Cone + Surface area of Cylinder

Now put value of Lateral Surface area of Cone and Surface area of Cylinder

Surface Area of Solid = 71.5 m²+ 187 m²

Surface Area of Solid = 258.5 m²

Nearest Surface Area of Solid = 259 m²

Chapter 10.6, Problem 29E

Chapter 10.6, Problem 32E

Chapter 10 Solutions

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

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