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51.

Describe how the two figures at the right are alike and how they are different. Which box has larger surface area?

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52. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

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53. The lateral surface area of a hollow cylinder is 4224 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

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54.
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

The road roller is cylinder.
Radius = $84 over 2 cm space equals space 42 space cm$
Length (h) = 1m = 100 cm
∴ Lateral surface area = $space 2 πrh$
= $2 cross times 22 over 7 cross times 42 cross times 100 space cm squared$
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= 26400 cm²
∴ Area levelled by the roller in 1 revolution = 26400 cm²
or Area levelled in 750 revolutions = 750 x 26400 cm²
= $fraction numerator 750 cross times 26400 over denominator 100 cross times 100 end fraction straight m squared$
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Thus, the required area of the road = 1980 m²

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55. A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container as shown in the figure. If the label is placed 2 cm from top and bottom, what is the area of the label?

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56. The length, breadth and height of a cuboid are 20 cm, 15 cm and 10 cm respectively. Find its total surface area.

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57. An aquarium is in the form of a cuboid whose external measures are 80 cm x 30 cm x 40 cm. The base, side faces and back faces are to be covered with a coloured paper. Find the area of the paper needed.

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58. The internal measures of a room are 12 m x 8 m x 4 m. Find the total cost of white washing all four walls of a room if the cost of white washing is Rs 5 per m². What will be the cost of white washing if the ceiling is also white washed?

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59. In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m².

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