Volume and Surface Area - Aptitude Questions and Answers Part 2

6. A company wants its sticker to be pasted on the outer surface of open drums it produces, leaving the top and the bottom bare. Dimensions of the drum are, diameter 40 cm and height 7 m. The cost of putting up these stickers is Rs 20/sq.m. Find the total cost of putting up the sticker on the drum.

a. Rs. 176
b. Rs. 352
c. Rs. 384
d. Rs. 480

Answer: a. Rs. 176

Explanation:

Tip:
Curved Surface Area of Cylinder = 2πrh
r - Radius and h - Height



Radius =40= 20 cm = 0.2 m
2
Curved Surface Area = 2 x22 x 0.2 x 7
7
∴ Curved Surface Area = 8.8 sq.m.
Cost of putting up the sticker = Rate x Area = 20 x 8.8 = Rs.176


7. Rajat makes 8 open cones of height 24 cm and slant height 25 cm from a sheet of thick paper. Find the area of the sheet.

a. 550 sq. m.
b. 4400 sq. m.
c. 6000 sq. m.
d. 6236 sq.m.

Answer: b. 4400 sq. m.

Explanation:

Tip:
Curved Surface Area of Cone = πrL
r - Radius and L - Slant Height
And, L = r2+h2
Where, h = Height



L2 = r2 + h2 ------------> from diagram of cone
∴ r2 = 252 - 242
∴ r = 7 cm
Curved surface area of cone =22x 7 x 25 = 550 sq.m.
7
Since the cone is open, it means, it just has curved surface.
One sheet can make 8 cones.
So area of one sheet = Curved surface area of 8 cones = 8 x 550
∴ Area of one sheet = 4400 sq.cm.


8. For the festive season, Rajesh wants to change the look of the conical caps he produces. While keeping the volume same, he want to increase their height to 9 times. What will be its effect in the radius?

a. Reduce to 1/9th
b. Reduce to 1/3rd
c. Increase to 3 times
d. Increase by 18 times

Answer: b. Reduce to 1/3rd

Explanation:

Tip:
Volume of Cone =1πr2h
3
r - Radius and h - Height




Volume must remain same.
∴1π(r1)2 h1 =1π(r2)2 h2
33
Now height becomes 9 times the original
∴ (r1)2 h1 = (r2)2 9 x h1
∴ r1 = 3r2
i.e. r2 =1r1 = Radius must become 1/3 rd
3


9. A spherical ball has a surface area of792sq. m. Find its volume.
7

a. 7 sq.cm.
b. 792/7 cu.cm.
c. 792π/7 cu.cm.
d. 792 cu.cm.

Answer: b. 792/7 cu.cm.

Explanation:

Tip:
Volume of solid sphere =4πr3
3
Surface area of sphere = 4πr2
r = Radius

Surface area =792= 4πr2
7
∴ r2 =792 x 7
7 x 4 x 22
∴ r = 3cm
Volume =4πr3 =4x22x 3 x 3 x 3 = 792/7 cu.cm.
337


10. 14 wooden boards of 2 cm thickness each are piled one above the other. On top of the 14th plate is kept a hemisphere that just covers it. Its diameter is 6 cm. Find the volume of the object we have just created.

a. 81 cu.cm
b. 144π cu.cm.
c. 270π cu.cm.
d. 360π cu.cm.

Answer: c. 270π cu.cm.

Explanation:

Tip:
Volume of hemisphere =2πr3
3
r = Radius
Volume of solid cylinder = πr2h
R = Radius and h = Height


14 plates (2cm thickness) on each other make a solid cylinder of (14 x 2 =) 28cm.
Hemisphere just covers the top plate.
Hence the diameter of the cylinder (wooden boards) will be same as the diameter of the hemisphere.
∴ Radius of Hemisphere = Radius of Cylinder =6= 3cm
2
Volume of object = Volume of Cylinder + Volume of Hemisphere
∴ Volume of object = π x 32 x 28 +2x π x 33 = 270π cu.cm.
3

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