Cube and volume and surface area
Geometry
Level
2
If a cube's edge is doubled then, what will be the ratio of new cube's volume TO original cube's volume ? Also the ratio between the lateral surface area of new cube's TO original cube's?
Note: Images not to scale.
(8:1) and (4:1)
(1:8) and (1:4)
(1:4) and (1:8)
(1:2) and (1:2)
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1 solution
LET EDGE = A
THUS ORIGINAL VOLUME= A^{3}
THUS ORIGINAL LATERAL SURFACE AREA = 4(A^{2})= 4A^{2}
NEW EDGE = 2A
THUS NEW VOLUME= (2A)^{3}= 8A^{3}
THUS NEW LATERAL SURFACE AREA = 4((2A)^{2}) = 4 * 8A^{2}
RATIO = NEW VOLUME / ORIGINAL VOLUME = 8A^{3}/ A^{3}= 8:1
RATIO = NEW LATERAL SURFACE AREA / ORIGINAL LATERAL SURFACE AREA = 4*8A^{2} / 4A^{2} = 4:1
THUS ANSWER = (8:1) AND (4:1)