# volume and surface area

11.

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
A.     3 : 7    B.     7 : 3
C.     6 : 7    D.     7 : 6

Explanation:

r2h     =     924             r =         924     x 2         = 7 m.
2rh     264     264

And, 2rh = 264         h =         264 x     7     x     1     x     1         = 6m.
22     2     7

Required ratio =     2r     =     14     = 7 : 3.
h     6

12.

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
A.     90 cm    B.     1 dm
C.     1 m    D.     1.1 cm

Explanation:

Let the thickness of the bottom be x cm.

Then, [(330 – 10) x (260 – 10) x (110 – x)] = 8000 x 1000

320 x 250 x (110 – x) = 8000 x 1000

(110 – x) =     8000 x 1000     = 100
320 x 250

x = 10 cm = 1 dm.

13.

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
A.     344.35 cm2    B.     462 cm2
C.     498.35 cm2    D.     None of these

Explanation:

h = 14 cm, r = 7 cm.

So, l = (7)2 + (14)2 = 245 = 75 cm.

Total surface area     = rl + r2

=         22     x 7 x 75 +     22     x 7 x 7     cm2
7     7
= [154(5 + 1)] cm2
= (154 x 3.236) cm2
= 498.35 cm2.

14.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
A.     2 : 1    B.     3 : 2
C.     25 : 18    D.     27 : 20

Explanation:

Volume of the large cube = (33 + 43 + 53) = 216 cm3.

Let the edge of the large cube be a.

So, a3 = 216         a = 6 cm.

Required ratio =         6 x (32 + 42 + 52)         =     50     = 25 : 18.
6 x 62     36

15.

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A.     5600    B.     6000
C.     6400    D.     7200