The figure shows the amount of water in two rectangular tanks, U and V, at first. Nick poured
13 of the water from U into V to fill it to the top, without overflowing.
- How much water was there in Tank U at first?
- Nick then poured all the water from Tank V into Tank U. 320 cm3 of water overflowed from Tank U. What was the height of Tank U?
(a)
Volume of water to fill Tank V
= 20 x 16 x 17
= 5440 cm
3
13 of volume of water in Tank U at first = 5440 cm
3
33 of volume of water in Tank U at first = 3 x 5440 = 16320 cm
3 Volume of water in Tank U at first = 16320 cm
3 Volume of water in Tank V at first
= 20 x 16 x 19
= 6080 cm
3 Total volume of water in Tank U and Tank V
= 16320 + 6080
= 22400 cm
3 Final volume of water in Tank U after 320 cm
3 of water overflowed
= 22400 - 320
= 22080 cm
3 Base area of Tank U
= 24 x 20
= 480 cm
2 Height of Tank U
= 22080 ÷ 480
= 46 cm
Answer(s): (a) 16320 cm
2 ; (b) 46 cm