Hw 31 surface area of pyramids and cones

1)LSA=219.91 m^2

 TSA= 298.45 m^2

2)LSA=785.39 ft^2

  TSA= 1099.55 ft^2

3)LSA=527.78 in^2

TSA=728.84 in^2

4)LSA=480.66 mm^2

TSA= 735.13 mm^2

5)LSA= 56 cm^2

  TSA= 72 cm^2

6)LSA=261 in^2

  TSA=391.5 in^2

Step-by-step explanation:

lateral surface area(LSA) of cone is calculated by: πrl

Total surface area(TSA) of cone is calculated by: πrl + πr^2

where r is radius of cone

           l is slant height of cone

Q1)

r=5m and l=14m

Putting value in formula:

LSA= πx 5x 14

      = 219.91

TSA= πx 5x 14 + π(5)^2

     = 298.45

Q2)

r=10ft and l=25ft

Putting value in formula:

LSA= πx 10x 25

      = 785.39

TSA= πx 10x 25 + π(10)^2

       = 1099.55

Q3)

r=8in and l=21in

Putting value in formula:

LSA= πx 8x 21

      = 527.78 in

TSA= πx 8x 21 + π(8)^2

     = 728.84

Q4)

r=9mm and l=17mm

Putting value in formula:

LSA= πx 9x 17

      = 480.66 mm

TSA= πx 9x 17 + π(9)^2

      = 735.13

Q5)

LSA of Pyramid is given by= 1/2(p)(l)

TSA of Pyramid is given by= 1/2(p)(l) +B

where p is perimeter of base

           B is area of base

and      l is slant height

Finding p= 4.length of each side       (as it is square base)

               =4x4

               = 16

finding B= s^2

             = 4^2

             =16

Putting values in formula:

LSA= 1/2(7)(16)

      = 56

TSA=1/2(7)(16) + 16

      = 72

Q6)

Finding p= 5.length of each side        (as it is Pentagon)

               =4x8.7

               = 34.8

finding B= 5[1/2(b)(h)]

             = 5[1/2(8.7)(6)]

             =130.5

Putting values in formula:

LSA= 1/2(34.8)(15)

      = 261

TSA=1/2(34.8)(15) + 130.5

      = 391.5 !

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the answer is 31.27mph