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Free_Kalibri [48]
2 years ago
9

New streetlights will be installed along a section of the highway. The posts for the streetlights will be 7.5 m tall and made of

aluminium. The city can choose to buy the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminium 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminium 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminium is 2.7 g/cm³, and the cost of aluminium is $0.38 per kilogram.
Part A: if all posts must be the same shape, which post design will cost the town less?
Part B: How much money will be saved per streetlight post design will cost the town less?
Mathematics
1 answer:
SIZIF [17.4K]2 years ago
6 0
First, we determine the volumes of the posts may it be cylindrical in shape or rectangular prism. 

(A) cylindrical:
                         ( π(26.7/100)² - π(24.2/100)²)*(7.5) = 0.3 m³
(B) rectangular prism:
                          (40/100)²(7.5) - (35/100)²(7.5) = 0.28125 m³

Then, we calculate for the amount of substance
 (A) cylindrical:   (0.3 m³)(2700 kg/m³) = 810 kg
 (B) rectangular prism : (0.28125 m³)(2700 kg/m³) = 759.375 kg

Then, calculate for the costs
 (A) (810 kg)($0.38/kg) = $307.8
 (B) (759.375 kg)($0.38/kg) = $288.56

Thus, the answer for A is rectangular post 
B. About $19.24 can be saved. 
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Counting numbers from 101 to 200, those with 6 as a digit are 19

<h3>The numbers</h3>

Let's start by listing all the number between 101 and 200

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Now, let's count the numbers with 6 as a digit

= 19 numbers has 6 as a digit

Thus, counting numbers from 101 to 200, those with 6 as a digit are 19

Learn more about counting numbers here:

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3, 9, 15, 21, 27 are your answers

3 x 1 = 3
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hope this helps
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