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jc624826
27.09.2019 •
Mathematics
Two rectangular prisms have a combined volume of 432 cubic feet. prism a has half the volume of prism b.
a. what is the volume of prism a? prism b?
b. if prism a has a base area of 24 ft², what is the height of prism a?
c. if prism b’s base is 2/3 the area of prism a’s base, what is the height of prism b?
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Ответ:
a. 144 cubic foot
b. 12 ft
c. 18 ft
Step-by-step explanation:
Let the volume of prism A be V_a
and that of prism b be V_b
ATQ, V_a + V_b= 432
also V_a= 0.5 V_b
⇒1.5 V_b= 432
= V_b= 432/1.5= 288 cubic feet
therefore V_a= 144 cubic feet
volume of prism= area of base×height = V_a
24×h = 144
⇒h= 12 ft
A_b= 2/3×24
⇒base area of prism B= 16 sq.ft
now 16×h_b= 288⇒h_b= 288/16= 18 ft
Ответ:
So the answer would be 14 cases bought
Hope I helped!