The figure shows the amount of water in two rectangular tanks, U and V, at first. Luke poured
14 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?
- Luke then poured all the water from Tank V into Tank U. 5184 cm3 of water overflowed from Tank U. What was the height of Tank U?
(a)
Volume of water to fill Tank V
= 18 x 14 x 16
= 4032 cm
3
14 of volume of water in Tank U at first = 4032 cm
3
44 of volume of water in Tank U at first = 4 x 4032 = 16128 cm
3 Volume of water in Tank U at first = 16128 cm
3 Volume of water in Tank V at first
= 18 x 14 x 18
= 4536 cm
3 Total volume of water in Tank U and Tank V
= 16128 + 4536
= 20664 cm
3 Final volume of water in Tank U after 5184 cm
3 of water overflowed
= 20664 - 5184
= 15480 cm
3 Base area of Tank U
= 20 x 18
= 360 cm
2 Height of Tank U
= 15480 ÷ 360
= 43 cm
Answer(s): (a) 16128 cm
2 ; (b) 43 cm