Question

Mr. Sandeep Kalra is a social worker. He always works for the welfare of his welfare of his village. In his village, there was no school building. Sandeep gave a rectangular plot of land for the school building. the length and breadth of the plot are 150m and 100m. the villagers with the help of Mr. Sandeep made the school in the shape of a cuboid whose dimensions are 50m*40m*15m.they also fenced the plot at rs 50 per m.

i) Find the area of the plot
ii)Find the base area of the school.
iii)what is the volume of the building?
iv)find the perimeter of the plot.
v)what is the cost of the fencing the plot

Answer 1

i) The area of the plot of land is 15,000 m²

ii) The base area of the school is 2,000 m²

iii) The volume of the school building is 30,000 m³

iv) The perimeter of the plot of land is 500 m

v) The cost of fencing the plot of land is Rs 2,500

Explanation:

The parameters of the land, the school building and the cost of fencing are;

The length of the land, l = 150 m

The breadth of the land, b = 100 m

The dimensions of the school = 50 m × 40 m × 15 m

The cost of fencing the plot per meter = Rs 50 per meter

i) The area of the plot of land, A = Length × Breadth

∴ A = 150 m × 100 m = 15,000 m²

The area of the plot of land, A = 15,000 m²

ii) Taking the height of the school, h = 15 m, the length of the school building,
`l_B` = 50 m, and the breadth of the school building,
`b_B` = 40 m, the base area of the school,
`A_B`, is given as follows;

`A_B` =
`l_B` ×
`b_B`

∴
`A_B` = 50 m × 40 m = 2,000 m²

iii) The volume of the school building, V = h ×
`l_B` ×
`b_B`

∴ V = 15 m × 50 m × 40 m = 30,000 m³

iv) The perimeter of the plot of land, P = 2 × l + 2 × b

∴ P = 2 × 150 m + 2 × 100 m = 500 m

The perimeter of the plot of land, P = 500 m

v) The cost of fencing the plot of land, C = P × (The cost of fencing the plot per meter )

∴ C = 500 m × Rs 50/m = Rs 2,500

The cost of fencing the plot of land, C = Rs 2,500