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16.12.2021 •
Mathematics
Of the 130 eighth graders at Franklin Middle school, 30 students play in the band, 22 students acted in the school play, and 12 of these students did both. How many are neither in the band nor acted in the play?
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Ответ:
Question
A rectangular pyramid has a height of 5 units and a volume of 60 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.
b) A rectangular prism in which BA = 12 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.
c) A rectangular prism in which BA = 36 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.
d) A rectangular prism in which BA = 12 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.
a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.
Step-by-step explanation:
The formula for the volume of a Rectangular Pyramid = 1/3 × Base Area × Height
In the question,
Base Area = ?
Height = 5 units
Volume = 60 units³
So,
60= 1/3 × BA × 5
Cross Multiply
180 = 5BA
BA = 180/5
BA = 36 units²
Also, the Volume of a Rectangular Prism =
Base Area × Height
From the above question
Base Area = 36 units²
Height = 5 units
Volume of the Rectangular prism = 36 units² × 5 units
= 180 units³
Therefore , the statement that explains whether Shannon is correct is option a,
" A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.