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Long Answer Type

41. Two cubes each with side b are joined to form a cuboid figure. What is the surface area of this cuboid? Is it 12b²? Is the surface area of cuboid formed by joining three such cubes, 18b²? why?

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42. How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area?

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Short Answer Type

43.

After the surface area of a cube is painted the cube is cut into 64 smaller cubes of same dimensions. How many have no face painted? 1 face painted? 2 faces painted? 3 faces painted?

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44. Find total surface area of the following cylinders.

(i) We have
Radius (r) = 14 cm
Height (h) = 8 cm
∴ Total surface area = $2 πr left parenthesis straight r plus straight h right parenthesis$

= $2 cross times 22 over 7 cross times 14 cross times left parenthesis 14 plus 8 right parenthesis space cm squared$

= $2 cross times 22 over 7 cross times 14 cross times 22 space cm squared$

= $space 2 cross times 22 cross times 2 cross times 22 space cm squared$

= $1936 space cm squared$

(ii) We have $straight r equals 3 over 2 space equals space 1 space straight m space and space straight h space equals space 2 space straight m$
∴ Total surface area = $2 πr left parenthesis straight r plus straight h right parenthesis$

= $2 cross times 22 over 7 cross times 1 cross times left parenthesis 1 plus 2 right parenthesis space straight m squared$

= $fraction numerator 2 cross times 22 cross times 3 over denominator 7 end fraction straight m squared$

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45.

Note that lateral surface area of a cylinder is the circumference of base x height of cylinder. Can we write lateral surface area of a cuboid as perimeter of base x height of cuboid?

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46. There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

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47. A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

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48. Find the side of a cube whose surface area is 600 cm².

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49. Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except bottom of the cabinet.

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50. Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m² of area is painted. How many cans of paint will she need to paint the room ?

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