A building in the shape of a rectangular pyramid is used to store construction stones. The building has a volume of 21,000 ft3 . A new building is being designed. It will also be in the shape of a rectangular pyramid, but compared to the existing building, the length of its base will be scaled by a factor of 23 , and the width of its base will be scaled by a factor of 53 . The height of the new building will be scaled such that the volume of the new building will be the same as the existing building. What scale factor will be used for the height of the new building?
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Step-by-step explanation:
Replace the formula with the given numbers. H = 60 cubic cm / (4 cm x 6 cm) / 3. H = 60 cubic cm / (24 cm squared / 3). H = 60 cubic cm / 8 cm squared. H = 7.5 cm. The height of a rectangular-based pyramid with volume of 60 cubic cm, length of 4 cm and width of 6 cm is 7.5 cm.
Check you answer by completing the formula with the values. V = 1/3 x (L x W x H). 60 cm3 = 1/3 x (4 cm x 6 cm x 7.5 cm). 60 cubic cm = 1/3 x 180 cubic cm. 60 cubic cm = 60 cubic cm and the formula balances out.
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