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10 May 2021, 22:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:58) correct
42%
(02:25)
wrong
based on 50
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Two equilateral triangles, each of area (√3), and three squares were combined to form the figure above. If this figure were to be cut out of paper and folded to form a prism of triangular base, what would be the volume of the prism?
A. 2
B. 3
C. 2√3
D. 4√3
E. 6
Attachment:
1.png [ 2.77 KiB | Viewed 2193 times ]
16 May 2021, 03:30
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Bunuel
The volume of a prism is (area of the base)*(height).
The area of equilateral triangle is \(side^2*\frac{\sqrt{3}}{4}\). Thus we have that \(side^2*\frac{\sqrt{3}}{4}=\sqrt{3}\) --> \(side=2\).
From the image given we can infer that the side of the triangles is also the side of the squares. Since the side of the square is the height of the prism, then the volume of the prism is (area of the base)*(height) = \(\sqrt{3}*2\).
Answer: C.
Attachment:
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General Discussion
11 May 2021, 00:15
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Given :
Area of equilateral triangle = (√3)
Considering each side of the triangle = a
Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>
Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2
Area of the base of the prism = a^2 = 4
Height of prism = √3
Volume of a triangular prism = Height of prism * area of the base
= √3 * 4
Answer : Volume = 4√3
IMO D
Area of equilateral triangle = (√3)
Considering each side of the triangle = a
Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>
Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2
Area of the base of the prism = a^2 = 4
Height of prism = √3
Volume of a triangular prism = Height of prism * area of the base
= √3 * 4
Answer : Volume = 4√3
IMO D
