Question

Length of a box is four times its height and its breadth is 3 times its height. The cost of white washing the walls at the rate of rs4 per meter sq. is rs6. Find the cost of tiling the floor at the rate of rs10 per m sq.​ (class 9 surface areas and volume)​

Answer 1

Given :-

▪ Length of a box is four times its height and its breadth is 3 times its height.

▪ The cost of white washing the walls at the rate of ₹ 4 per m² is ₹ 6.

To Find :-

▪ Cost of tiling the floor at the rate of ₹ 10 per m²

Solution :-

First of all, Let's arrange the measurements of the box in terms of its height as given in the question,

Let the height of the box be h.

Given,

⇒ Length = 4 × Height

⇒ Length = 4h

Also,

⇒ Breadth = 3 × Height

⇒ Breadth = 3h

Since the box is in cuboid shape, so

⇒ Area of walls = (Total surface area) - (2 × Area of floor)

⇒ Area of walls = 2(LB + BH + LH) - 2LB

⇒ Area of walls = 2(BH + LH)

⇒ Area of walls = 2(3h×h + 4h×h)

⇒ Area of walls = 2(3h² + 4h²)

⇒ Area of walls = 14h²

We are given the cost and rate of white washing the walls, We know

⇒ Cost = Area × Rate

⇒ 6 = 14h² × 4

⇒ 3/28 = h² ...(1)

Now, we have to find the cost of tiling the floor at the rate of ₹ 10 per m²

⇒ Area = LB

⇒ Area = 4h × 3h

⇒ Area = 12h²

⇒ Area = 12 × 3/28 [ from (1) ]

⇒ Area = 18 / 14 m²

⇒ Area = 9/7 m²

Now, we are given the rate of tiling the floor so,

⇒ Cost = Rate × Area

⇒ Cost = 10 × 9/7

⇒ Cost = ₹ 12.85

Hence, The cost of tiling the floor is ₹ 12.85

Answer 2

Step-by-step explanation:

ANSWER ✍️

Given :-

▪ Length of a box is four times its height and its breadth is 3 times its height.

▪ The cost of white washing the walls at the rate of ₹ 4 per m² is ₹ 6.

To Find :-

▪ Cost of tiling the floor at the rate of ₹ 10 per m²

Solution :-

First of all, Let's arrange the measurements of the box in terms of its height as given in the question,

Let the height of the box be h.

Given,

⇒ Length = 4 × Height

⇒ Length = 4h

Also,

⇒ Breadth = 3 × Height

⇒ Breadth = 3h

Since the box is in cuboid shape, so

⇒ Area of walls = (Total surface area) - (2 × Area of floor)

⇒ Area of walls = 2(LB + BH + LH) - 2LB

⇒ Area of walls = 2(BH + LH)

⇒ Area of walls = 2(3h×h + 4h×h)

⇒ Area of walls = 2(3h² + 4h²)

⇒ Area of walls = 14h²

We are given the cost and rate of white washing the walls, We know

⇒ Cost = Area × Rate

⇒ 6 = 14h² × 4

⇒ 3/28 = h² ...(1)

Now, we have to find the cost of tiling the floor at the rate of ₹ 10 per m²

⇒ Area = LB

⇒ Area = 4h × 3h

⇒ Area = 12h²

⇒ Area = 12 × 3/28 [ from (1) ]

⇒ Area = 18 / 14 m²

⇒ Area = 9/7 m²

Now, we are given the rate of tiling the floor so,

⇒ Cost = Rate × Area

⇒ Cost = 10 × 9/7

⇒ Cost = ₹ 12.85

Hence, The cost of tiling the floor is ₹ 12.85

hope this helps you!!

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