Question

1. A)Aflati latimea unui teren, forma dreptunghi, exprimat in metri, daca lungimea lui este de 0,8 km, iar aria este egala cu 800 ari b)aflati lungimea gardului din jurul terenului, de la punctul a 2.Un bazin are forma de cuboid cu lungimea de 5,5 m, latimea 32 dm si inaltimea 3m a)cate placi de teracota sunt necesare pentru a pava fundul bazinului, daca placile de teracota sunt pastrate cu lungimea de 20 cm? b)Cati metri cubi de apa incap in bazin?

Answer 1

`\large \boxed{\text{1. a) 100 m; b) 1.8 km; 2. a) 400 tiles; b) 48 m}^(3)}`

Explanation:

Q1.

a) Width of field

The formula for the area of a rectangle is

A = lw

Data

A = 800 a

l = 0.8 km

Calculations

(i) Convert all measurements to metres

A = 800 a × 100 m²/a = 80 000 m²

l = 0.8 km × 1000 m/1 km = 800 m

(ii) Calculate the width

`\begin{array}{rcl}A & = & lw\\80000 & = & 800w\\w & = & (80000)/(800)\\\\& = & \textbf{100 m}\\\end{array}\\\text{The width of the field is $\large \boxed{\textbf{100 m}}$}`

b) Perimeter of field

The formula for the perimeter of a rectangle is

`\begin{array}{rcl}P & = & 2(l + w)\\& = &2(800 + 100)\\& = & 2(900)\\& = & \text{1800 m}\\& = & \textbf{1.8 km}\\\end{array}\\\text{The length of the fence around the field is $\large \boxed{\textbf{1.8 km}}$}`

Q2.

a) Number of tiles

Data:

l = 5 m

w = 32 dm

h = 3 m

Tile edge = 20 cm

(i) Convert all measurements to metres

w = 32 dm × (1 m/10 dm) = 3.2 m

Tile edge = 20 cm × (1 m/100 cm) = 0.20 m

(ii) Area of pool bottom

`\begin{array}{rcl}A& = & 5* 3.2\\& = & \textbf{16 m}^(2)\\\end{array}`

(iii) Area of one tile

`\begin{array}{rcl}A & = & s^(2)\\ & = & 0.20^(2)\\& = & \textbf{0.04 m}^{\mathbf{2}}\\\end{array}`

(iv) Number of tiles

`\text{No. of tiles } = \text{16 m }^(2) * \frac{\text{1 tile}}{\text{0.04 m}^(2)} = \textbf{400 tiles}\\\text{It will take $\large \boxed{\textbf{400}}$ tiles to cover the bottom of the pool.}`

b) Volume of pool

The formula for the volume of a rectangular prism is\begin{array}{rcl}

`\begin{array}{rcl}V & = & lwh\\& = &5 * 3.2 * 3\\& = & \textbf{48 m}^(3)\\\end{array}\\\text{The volume of the pool is $\large \boxed{\textbf{48 m}^{\mathbf{3}}}$}`