Answer:
(i) 226 ltr
(ii) 2 m²
(iii) 16 cm
(iv) 178 ltr
Step-by-step explanation:
(i)
volume of a cylinder = [tex]\pi r^2h[/tex] (where r is the radius and h is the height)
Given:
- radius = 24 cm
- height = 125cm
⇒ volume = [tex]\pi[/tex] x 24² x 125 = 72000[tex]\pi[/tex] cm³
As there are 1000 cm³ in 1 liter
⇒ volume = 72000[tex]\pi[/tex] ÷ 1000 = 72[tex]\pi[/tex] ltr ≈ 226 ltr (nearest whole number)
(ii)
Surface area of cylinder open at one end = [tex]\pi r^2+2\pi rh[/tex]
Given:
- radius = 24 cm
- height = 125cm
⇒ surface area = [tex]\pi \times24^2+2\pi \times24\times125[/tex]
⇒ surface area = [tex]6576\pi[/tex] cm²
As there are 10000 cm² in 1 m²
⇒ surface area = [tex]6576\pi[/tex] ÷ 10000 = 2.065911... ≈ 2 m²
(iii)
Volume of a rectangular prism = l x w x h
(where l is the length, w is the width and h is the height)
Given:
- length = 150 cm
- width = 20 cm
- volume = 48000 cm³
⇒ 48000 = 150 x 20 x h
⇒ 48000 = 3000h
⇒ h = 48000 ÷ 3000 = 16 cm
(iv)
Difference in capacity is the difference in volume
Volume of cylinder in liters = 226 ltr
Volume of trough in liters = 48000 ÷ 10000 = 48 ltr
⇒ difference = 226 - 48 = 178 ltr
