sat suite question viewer

Geometry and Trigonometry Difficulty: Hard

A right square prism has a height of $14$ units. The volume of the prism is $2,016$ cubic units. What is the length, in units, of an edge of the base?

Back question 156 of 268 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Explanation

The correct answer is $12$ . The volume, $V$ , of a right square prism can be calculated using the formula $V = s^{2} h$ , where $s$ represents the length of an edge of the base and $h$ represents the height of the prism. It’s given that the volume of the prism is $2,016$ cubic units and the height is $14$ units. Substituting $2,016$ for $V$ and $14$ for $h$ in the formula $V = s^{2} h$ yields $2,016 equals left parenthesis s squared right parenthesis left parenthesis 14 right parenthesis$ . Dividing both sides of this equation by $14$ yields $144 equals s squared$ . Taking the square root of both sides of this equation yields two solutions: $- 12 = s$ and $12 equals s$ . The length can't be negative, so $12 equals s$ . Therefore, the length, in units, of an edge of the base is $12$ .