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23 Nov 2020, 01:15
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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:
5%
(low)
Question Stats:
90% (01:24) correct
10%
(02:11)
wrong
based on 78
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A container in the shape of a rectangular solid with dimensions 5, 5, and 12 has four times the volume of a cylindrical container with radius 3. What is the height of the cylinder?
A. \(\frac{25}{\pi}\)
B. \(\frac{25}{2\pi}\)
C. \(\frac{25}{3\pi}\)
D. \(\frac{25}{4\pi}\)
E. \(5\pi\)
A. \(\frac{25}{\pi}\)
B. \(\frac{25}{2\pi}\)
C. \(\frac{25}{3\pi}\)
D. \(\frac{25}{4\pi}\)
E. \(5\pi\)
23 Nov 2020, 02:38
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Explanation:
Volume of rectangular solid = 5x5x12 = 300
Volume of Cylindrical container = π*r^2*h = 9πh
Volume of rectangular solid = 4 x Volume of Cylindrical container
300 = 4 x 9πh
75 = 9πh
25 = 3πh
h = 25/3π
IMO-C
Volume of rectangular solid = 5x5x12 = 300
Volume of Cylindrical container = π*r^2*h = 9πh
Volume of rectangular solid = 4 x Volume of Cylindrical container
300 = 4 x 9πh
75 = 9πh
25 = 3πh
h = 25/3π
IMO-C
23 Nov 2020, 03:55
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CONCEPT: Volume of 3D figures:
Volume of a cylinder = ∏r2h
(“r” being the radius and “h” being the height of the cylinder)
Volume of a rectangular container= l.b.h
(l,b,h being the length, breadth and height of the container)
Volume of the rectangular container =5*5*12 =300 unit3
Volume of the cylinder = ∏(9)h
Four times this volume = 4 * ∏(9) h = 36∏h
According to the question:
36∏h = 300
=>h= 300/36 * ∏
=25/3∏ (C)
Hope this helps. Keep studying.
Volume of a cylinder = ∏r2h
(“r” being the radius and “h” being the height of the cylinder)
Volume of a rectangular container= l.b.h
(l,b,h being the length, breadth and height of the container)
Volume of the rectangular container =5*5*12 =300 unit3
Volume of the cylinder = ∏(9)h
Four times this volume = 4 * ∏(9) h = 36∏h
According to the question:
36∏h = 300
=>h= 300/36 * ∏
=25/3∏ (C)
Hope this helps. Keep studying.
