theotis had to load a truck with television sets . the cargo area of the truck is a rectangular prism that measures 81ft by 21ft by 11ft. each tv measures 1&1/2 by 1&2/3 by 1&1/3. how many sets can be loaded into the truck?
Theotis had to load a truck with television sets . The cargo area of the truck is a rectangular prism that measures 81ft by 21ft by 11ft. Each tv measures 1&1/2ft by 1&2/3ft by 1&1/3ft. How many sets can be loaded into the truck?
To find out how many television sets can be loaded into the truck, we need to calculate the volume of the cargo area and divide it by the volume of each television set.
First, let's calculate the volume of the cargo area:
Volume = length x width x height
Volume = 81 ft x 21 ft x 11 ft
Volume = 18,171 ft³
Next, let's calculate the volume of each television set:
Volume = length x width x height
Volume = (1 & 1/2) ft x (1 & 2/3) ft x (1 & 1/3) ft
Volume = (3/2) ft x (5/3) ft x (4/3) ft
Volume = 20/6 ft³
Volume = 10/3 ft³
Volume = 3 & 1/3 ft³
Now, let's calculate how many television sets can fit into the truck by dividing the volume of the cargo area by the volume of each television set:
Number of sets = Volume of cargo area / Volume of each television set
Number of sets = 18,171 ft³ / (3 & 1/3) ft³
Number of sets = 18,171 ft³ / (10/3) ft³
Number of sets = 18,171 ft³ x 3 ft³ / 10 ft³
Number of sets = 54,513 ft³ / 10 ft³
Number of sets = 5,451.3 sets (rounded to the nearest whole number)
Therefore, approximately 5,451 television sets can be loaded into the truck.