Question

Paintinpainting a room of length 6 m and 8m cost of rupees 320 @ rupees 2 per metre square find the height of the little surface areag

Answer 1

For the cubical box

           ∵Edge of the cubical box = 10 cm

           ∴ Lateral surface area = 4a2

                 = 4 × 102 cm2

                 = 4 × 100 cm2

                 = 400 cm2

           Total surface area = 6a2

           = 6 × 102 = 6 × 100 cm2

           = 600 cm2

           ∵For the cuboidal box, l = 12.5 cm, b = 10 cm, h = 8 cm

           ∴ Lateral surface area = 2[(l + b)] × h

                 = 2[12.5 + 10] × 8 cm2

                 = 2[22.5 × 8] cm2

                 = 360 cm2

           Total surface area = 2[lb + bh + hl]

           = 2[(12.5 × 10) + (10 × 8) + (8 × 12.5)] cm2

           = 2[125 + 80 + 100] cm2

           = 2[305] cm2 = 610 cm2

           Obviously,

           (i) ∵ 400 cm2 > 360 cm2 and 400 – 360 = 40

                 ∴ The cubical box, has greater lateral surface area by 40 m2.

           (ii) ∵ 610 cm2 > 600 cm2 and 610 – 600 = 10

                 ∴The cuboidal box has greater total surface area by 10 m2.