Exercise 14.1

1. There are two cuboidal boxes as shown in the given figure. Which box requires the less amount of material to make?

Solution:

To determine which box requires less material, we need to calculate the surface areavolume of each box.

The surface area of a cuboid is given by the formula: Surface Area = (lw + wh + lh)

where l is the length, w is the width, and h is the height.

(a) Box Dimensions:

Length (l) = cm

Width (w) = cm

Height (h) = cm

Surface Area (a) = 2(60 × 40 + 40 × 50 + 60 × 50)

= 2( + + )

= 2()

= sq cm

(b) Box Dimensions:

Length (l) = cm

Width (w) = cm

Height (h) = cm

Surface Area (b) = 2(50 × 50 + 50 × 50 + 50 × 50)

= 2( + + )

= 2()

= sq cm

Comparing the surface areas:

Surface Area (a) = 14800 sq cm

Surface Area (b) = 15000 sq cm

Since 14800 15000, box requires less material to make.

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

Solution:

Surface area of a cube = × side2

600 = 6 × side2

side2 =

Side = cm

3. Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m. Find the surface area she covered if she painted all surfaces except the top and bottom of the cabinet?

Solution:

Surface area of a cuboid = (lw + wh + lh)

Given dimensions: l = m, w = m, h = m

Area of top and bottom = 2 × (l × w) = 2 × ( × ) = m2

Total surface area = 2(2 × 1 + 1 × 1.5 + 2 × 1.5) = 2( + + ) = 2() = m2

Area painted = Total surface area - Area of top and bottom = - = m2

4. Find the cost of painting a cuboid of dimensions 20 cm × 15 cm × 12 cm at the rate of 5 paisa per square centimeter.

Solution:

Surface area of cuboid = 2(20 × 15 + 15 × 12 + 20 × 12) = 2( + + ) = 2() = cm2

Cost of painting = 1440 × = paisa = Rs.