Volume of cube & cuboid - Wiki

  • #volumeofcube
    • A rectangular tank was half-filled with water. When `4.5l` of water was added, it became `4/5` full. What was the height of the tank if its base area was `500` cm`^2`?
      • #volumeofcube&cuboid

        Difference

        `4/5`  -  `1/2` = `8/10` - `5/10` = `3/10`

        `3/10`  of  tank = 4.5l

        `10/10` of tank = (4.5 `-:` 3) `xx` 10 = 15l

        15l = 15000ml = 15000 cm2

        Height of tank

        15000 `-:` 500 = 30 cm
                    

    • The solid below is made up of 1-cm cubes. What is the volume of the solid? Ans: _BLANK_ cm`^3`
      • #volumeofcube&cuboid

        No. of cubes

        7 + 2 + 1 = 10

        vol. of 1-cm cubes

        `xx` 1 `xx` 1 = 1cm3

        vol. of solid

        10 `xx` 1 = 10 cm3 

    • A tank measuring 60 cm by 10 cm by 24 cm is `1/4` filled with water. Taps X and Y were turned on at the same time. Water was drained out from Tap X at the rate of 750 cm`^3` per minute while water flowed in from Tap Y at the rate of 1050 cm`^3` per minute. (a) How much more water is needed to fill the tank to the brim? (b) How long would it take to fill the tank to the brim? Ans: (a) _BLANK_ ml [1] Ans: (b) _BLANK_ [3]
      • #volumeofcube&cuboid

        (part a):

        Fraction of water needed to fill tank

        `4/4`  - `1/4`  = `3/4`

        Amt. of water needed to fill tank

        60 `xx` 10 `xx` 24 `xx` `3/4`

        14400 `xx` `3/4`

        10800 ml

        (part b):

        Effective filling rate (difference between tap X and Y)

        1050 - 750 = 300cm3

        Amt. of minutes to fill up tank

        10800 `-:` 300 = 36 mins         

         

         

         

    • The figure below shows a transparent rectangular container partially filled with unit cubes. How many cubes can the container hold altogether?
      • #volumeofcube&cuboid

        Currntly no. of cubes

        7 + 3 + 1 = 11

        Total no. of cubes container can hold

        `xx` 3 `xx` 3 = 36  

    • The base area of a rectangular tank is 20 m`^2`. The tank contains 120 m`^3` of water when it is `3/4` filled. What is the height of the tank? Ans: _BLANK_ m
      • #volumeofcube&cuboid

        Current height of water

        120 `-:` 20 = 6 m

        6 cm = `3/4`  filled 

        `1/4`  filled = 6 `-:` 3 = 2 m

        `4/4`  filled = 2 `xx` 4 = 8 m