Question

Please answer this question ​

Answer 1

(i) 226 ltr

(ii) 2 m²

(iii) 16 cm

(iv) 178 ltr

Explanation:

(i)

volume of a cylinder =
`\pi r^2h` (where r is the radius and h is the height)

Given:

• radius = 24 cm
• height = 125cm

⇒ volume =
`\pi` x 24² x 125 = 72000
`\pi` cm³

As there are 1000 cm³ in 1 liter

⇒ volume = 72000
`\pi` ÷ 1000 = 72
`\pi` ltr ≈ 226 ltr (nearest whole number)

(ii)

Surface area of cylinder open at one end =
`\pi r^2+2\pi rh`

Given:

• radius = 24 cm
• height = 125cm

⇒ surface area =
`\pi *24^2+2\pi *24*125`

⇒ surface area =
`6576\pi` cm²

As there are 10000 cm² in 1 m²

⇒ surface area =
`6576\pi` ÷ 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