The figure shows the amount of water in two rectangular tanks, U and V, at first. Archie 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?
- Archie then poured all the water from Tank V into Tank U. 6840 cm3 of water overflowed from Tank U. What was the height of Tank U?
(a)
Volume of water to fill Tank V
= 20 x 18 x 17
= 6120 cm
3
13 of volume of water in Tank U at first = 6120 cm
3
33 of volume of water in Tank U at first = 3 x 6120 = 18360 cm
3 Volume of water in Tank U at first = 18360 cm
3 Volume of water in Tank V at first
= 20 x 18 x 20
= 7200 cm
3 Total volume of water in Tank U and Tank V
= 18360 + 7200
= 25560 cm
3 Final volume of water in Tank U after 6840 cm
3 of water overflowed
= 25560 - 6840
= 18720 cm
3 Base area of Tank U
= 24 x 20
= 480 cm
2 Height of Tank U
= 18720 ÷ 480
= 39 cm
Answer(s): (a) 18360 cm
2 ; (b) 39 cm