Answer :
Answer:
[tex]\large \boxed{\text{1. a) 100 m; b) 1.8 km; 2. a) 400 tiles; b) 48 m}^{3}}[/tex]
Step-by-step 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
[tex]\begin{array}{rcl}A & = & lw\\80000 & = & 800w\\w & = & \dfrac{80000}{800}\\\\& = & \textbf{100 m}\\\end{array}\\\text{The width of the field is $\large \boxed{\textbf{100 m}}$}[/tex]
b) Perimeter of field
The formula for the perimeter of a rectangle is
[tex]\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 $\large \boxed{\textbf{1.8 km}}$}[/tex]
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
[tex]\begin{array}{rcl}A& = & 5\times 3.2\\& = & \textbf{16 m}^{2}\\\end{array}[/tex]
(iii) Area of one tile
[tex]\begin{array}{rcl}A & = & s^{2}\\ & = & 0.20^{2}\\& = & \textbf{0.04 m}^{\mathbf{2}}\\\end{array}[/tex]
(iv) Number of tiles
[tex]\text{No. of tiles } = \text{16 m }^{2} \times \dfrac{\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.}[/tex]
b) Volume of pool
The formula for the volume of a rectangular prism is\begin{array}{rcl}
[tex]\begin{array}{rcl}V & = & lwh\\& = &5 \times 3.2 \times 3\\& = & \textbf{48 m}^{3}\\\end{array}\\\text{The volume of the pool is $\large \boxed{\textbf{48 m}^{\mathbf{3}}}$}[/tex]