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CAT 2017 Quantitative Ability
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© examsnet.com
Question : 20
Total: 34
A box is built vertically upwards from a base that is a regular hexagon of side 'a'. The height of the shapes is ‘h' If the height of this shape is doubled, the total surface area increases by 50%, find the ratio a: h
2 : 1
2
:
√
3
3
:
√
2
√
2
:
1
Validate
Solution:
Area of the box = area (2 hexagons) + area (6 rectangles).
=
6
√
3
4
a
2
×
2
+
6
×
a
h
=
3
√
3
a
2
+
6
a
h
In the revised box, the height becomes = 2h
New area =
6
√
3
4
a
2
×
2
+
6
×
a
×
2
h
=
3
√
3
a
2
+
12
a
h
Area has increased by 50%
⇒ New area = 1.5 x (old area)
⇒
(
3
√
3
a
2
+
6
a
h
)
15
=
3
√
3
a
2
+
12
a
h
⇒
3
√
3
a
2
×
15
+
9
a
h
=
3
√
3
a
2
+
12
a
h
⇒
3
√
3
a
2
×
05
=
3
a
h
⇒
√
3
2
a
=
h
⇒
a
h
=
2
√
3
⇒
a
:
h
=
2
:
√
3
© examsnet.com
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