Surface Areas and Volumes Test - 12

Let R and H respectively be the radius and the height of the cylinder.

Let r and h respectively be the radius and the height of the cone.

According to the given information:

Thus, the ratio of the volumes of the cylinder and the cone is 1: 4.

The correct answer is A.

Length of the edge of each cubical box = 20 cm

∴ Total surface area of each cubical box = 6 × (20 cm)² = 2400 cm²

The area of paper used in covering one box is equal to its total surface area.

∴ Area of paper used in covering 10 cubical boxes = (10 × 2400) cm² = 24000 cm²

Length (l) of each cuboidal box = 20 cm

Breadth (b) of each cuboidal box = 14 cm

Height (h) of each cuboidal box = 12 cm

Now, the total surface area of cuboid is given by, 2 (lb + bh + lh).

∴ Total surface area of each cuboidal box

= 2(20 cm × 14 cm + 14 cm × 12 cm + 20 cm × 12 cm)

= [2(280 + 168 + 240)] cm²

= (2 × 688) cm²

= 1376 cm²

∴ Area of paper used in covering 5 cuboidal boxes = (5 × 1376) cm² = 6880 cm²

∴ Area of paper used in covering all the boxes = (24000 + 6880) cm²

= 30880 cm²

Now, 100 cm = 1 m

⇒ 10000 cm² = 1 m²

⇒ 30880 cm² = 3.088 m²

Cost of 1 m² of glossy paper = Rs 5

∴ Cost of 3.088 m² of glossy paper = Rs (3.088 × 5) = Rs 15.44 ≈ Rs 15.40

Thus, the total cost of covering the boxes with glossy paper is Rs 15.40.

The correct answer is B.