The lateral surface area and total area of the regular pyramid.

Question

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Answer 1

Question

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

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Answer 2

Question

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

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Answer 3

Question

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

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Answer 4

Question

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

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Answer 5

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

Answer 6

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

Answer 7

Chapter 12, Problem 1RP

a

To determine

To calculate : The lateral surface area and total area of the regular pyramid.

Answer 8

a

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the regular pyramid are $60 units2$ and $96 units2$

Answer 9

a

Expert Solution

Answer 10

a

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

Side of the base square $(a)=6 units$

Slant height $(l)=5 units$

Formula used:

Lateral area $(LA)=4×(12×l×a)$

Total area $(TA)=(Lateral Area)+(Base Area)=4×(12×l×a)+(a2)$

Calculation:

Lateral area of the regular pyramid

$(LA)=4×(12×l×a)=4×(12×5×6)=4×(5×3)=60 (units)2$

Total area of the regular pyramid

$(TA)=4×(12×l×a)+(a2)=60+(6)2=60+36=96 (units)2$

Answer 13

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

Answer 14

b

To determine

To calculate : The lateral surface area and total area of the cylinder.

Answer 15

b

Expert Solution

Answer to Problem 1RP

The lateral surface area and total area of the cylinder are $56π units2$ and $154π units2$

Answer 16

b

Expert Solution

Answer 17

b

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

Base radius of the cylinder $(r)=4 units$

Height of the cylinder $(h)=7 units$

Formula used:

Lateral area $(LA)=2πrh$

Total area $(TA)=(2πrh)+(2πr2)$

Calculation:

Lateral area of cylinder

$(LA)=2πr×h=2π×4×7=56π (units)2$

Total area of cylinder

$(TA)=(2πr×h)+(2πr2)=56π+(2π×72)=56π+98π=154π (units)2$

Answer 20

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

The lateral surface area and total area of the regular pyramid.

To calculate : The lateral surface area and total area of the regular pyramid.

Answer to Problem 1RP

Explanation of Solution

To calculate : The lateral surface area and total area of the cylinder.

Answer to Problem 1RP

Explanation of Solution

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