Page 301 - Start Up Mathematics_8 (Non CCE)

14. The height of a right circular cylinder is 12.6 cm. Three times the sum of the areas of its two circular
faces is twice the area of the curved surface. Find the volume of the cylinder.
3
15. A piece of copper of volume 4.4 dm is drawn into a cylindrical wire 0.025 cm in diameter. Find the
length of the wire.
16. The diameter of a cylindrical tank is 24.5 m and depth is 8 m. How many metric tons of water will
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it hold? [1 m of water weighs 1,000 kg and 1 metric ton = 1,000 kg]
17. A hollow cylindrical tube, open at both ends is made of 2 cm thick iron. If the external diameter is
50 cm and the length of the tube is 140 cm, find the volume of iron in it. Find the weight of the tube,
3
if 1 cm of metal weighs 8 g.
18. A rectangular sheet of paper 35 cm × 21 cm can be transformed into the curved surface of a right
circular cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth.
Find the ratio of the volumes of the two cylinders thus formed.

AT a Glance

1. Cuboid Æ Length (l), Breadth (b), Height (h)
(i) Volume (V) of a cuboid = Length × Breadth × Height = l × b × h cubic units
(ii) Total surface area (TSA) of cuboid = 2(lb + bh + hl) sq. units
(iii) Lateral surface area (LSA) or area of four walls of cuboid = 2h(l + b) sq. units
2
2
2
(iv) Length of the diagonal of cuboid = l + b + h units
2. Cube Æ side (or edge) = a units
3
3
(i) Volume of cube = (Side) = a cubic units
2
2
(ii) Total surface area (TSA) of cube = 6 (Side) = 6a sq. units
2
2
(iii) Lateral surface area (LSA) of cube = 4 (Side) = 4a sq. units
(iv) Length of the diagonal of cube = 3 (side) = 3a units
3. Right Circular Cylinder Æ Radius (r), Height (h)
2
(i) Volume of right circular cylinder = pr h cubic units
(ii) Curved surface area (CSA) of right circular cylinder = 2prh sq. units
(iii) Total surface area (TSA) of right circular cylinder = 2pr(h + r) sq. units
4. Hollow Cylinder Æ External radius (R), Internal radius (r), Height (h)
2
2
(i) Volume of hollow cylinder = External volume – Internal volume = ph(R – r ) cubic units
2
2
(ii) Surface area of each base = p(R – r ) sq. units
(iii) Curved surface area (CSA) of hollow cylinder = 2ph(R + r) sq. units
(iv) Total surface area (TSA) of hollow cylinder = CSA + Surface area of 2 bases
= 2p(R + r)(h + R – r) sq. units.

Review Exercises

Multiple ChoiCe Questions
1. The volume of a cube whose edge is 3x is:
2
2
3
(a) 27x (b) 18x (c) 18x (d) 27x 3
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