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A rectangular container measures 20cm long, 30cm wide and 40cm high. Calculate its volume in litres.

Mathematics

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Step-by-step solution

24 steps

Part 19· 2 steps

A rectangular container measures 20cm long, 30cm wide and 40cm high. Calculate its volume in litres.

  1. Calculate the volume in cubic centimeters.

    The volume of a rectangular container is given by the formula V=length×width×heightV = \text{length} \times \text{width} \times \text{height}.

    V=20 cm×30 cm×40 cmV = 20\, \text{cm} \times 30\, \text{cm} \times 40\, \text{cm} V=24000 cm3V = 24000\, \text{cm}^3
  2. Convert the volume from cubic centimeters to litres.

    We know that 1 L=1000 cm31\, \text{L} = 1000\, \text{cm}^3.

    V=24000 cm31000 cm3/LV = \frac{24000\, \text{cm}^3}{1000\, \text{cm}^3/\text{L}} V=24 LV = 24\, \text{L}

    The correct option is (a).
    The volume of the container is 24 L\boxed{\text{24 L}}.

Part 20· 2 steps

A cyclist used 7 hours to cover a distance of 560km. Find his average speed.

  1. Use the formula for average speed.

    Average speed is calculated as Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.

    Speed=560 km7 hours\text{Speed} = \frac{560\, \text{km}}{7\, \text{hours}}
  2. Calculate the average speed.

    Speed=80 km/h\text{Speed} = 80\, \text{km/h}

    The correct option is (b).
    The cyclist's average speed is 80 km/h\boxed{\text{80 km/h}}.

Part 21· 2 steps

A rectangular tank has a length of 12cm, a breadth of 80cm, and a height of 50cm respectively. What is the volume of water in the tank when it is full?

  1. Calculate the volume of the rectangular tank.

    The volume of a rectangular tank is given by the formula V=length×breadth×heightV = \text{length} \times \text{breadth} \times \text{height}.

    V=12 cm×80 cm×50 cmV = 12\, \text{cm} \times 80\, \text{cm} \times 50\, \text{cm}
  2. Perform the multiplication.

    V=48000 cm3V = 48000\, \text{cm}^3

    None of the options (a) 982 cm³, (b) 582 cm³, (c) 672 cm³, (d) 472 cm³ match the calculated volume. There might be a typo in the question or options provided in the image. Assuming the question asks for the volume with the given dimensions, the calculated volume is 48000 cm348000\, \text{cm}^3. If the question intended to ask for volume in litres, it would be 48 L48\, \text{L}. Given the options are in cm³, the calculated value does not match. I will provide the calculated answer.
    The volume of water in the tank when it is full is 48000 cm3\boxed{\text{48000 cm}^3}.

Part 22· 2 steps

A motorist whose average speed was 56 km/h, covered a distance of 448 km. Find the time taken.

  1. Use the formula for time.

    Time is calculated as Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}.

    Time=448 km56 km/h\text{Time} = \frac{448\, \text{km}}{56\, \text{km/h}}
  2. Calculate the time taken.

    Time=8 hours\text{Time} = 8\, \text{hours}

    The correct option is (b).
    The time taken is 8 hours\boxed{\text{8 hours}}.

Part 23· 2 steps

How many weeks are in 364 days?

  1. Divide the total number of days by the number of days in a week.

    There are 7 days in a week.

    Number of weeks=364 days7 days/week\text{Number of weeks} = \frac{364\, \text{days}}{7\, \text{days/week}}
  2. Perform the division.

    Number of weeks=52 weeks\text{Number of weeks} = 52\, \text{weeks}

    The correct option is (d).
    There are 52 weeks\boxed{\text{52 weeks}} in 364 days.

Part 24· 1 step

Find the sum of 23.8, 49.72 and 189.77.

  1. Align the decimal points and add the numbers.

    23.8023.80 49.7249.72 +189.77+ 189.77 263.29‾\overline{263.29}

    The correct option is (a).
    The sum is 263.29\boxed{\text{263.29}}.

Part 25· 5 steps

Simplify: 64+4936+144−8116\frac{\sqrt{64} + 49}{\sqrt{36}} + \frac{\sqrt{144} - 81}{\sqrt{16}}

  1. Calculate the square roots.

    64=8\sqrt{64} = 8 36=6\sqrt{36} = 6 144=12\sqrt{144} = 12 16=4\sqrt{16} = 4
  2. Substitute the square root values into the expression.

    8+496+12−814\frac{8 + 49}{6} + \frac{12 - 81}{4}
  3. Perform the addition and subtraction in the numerators.

    576+−694\frac{57}{6} + \frac{-69}{4}
  4. Convert the fractions to decimals or find a common denominator.

    576=9.5\frac{57}{6} = 9.5 −694=−17.25\frac{-69}{4} = -17.25
  5. Add the two results.

    9.5+(−17.25)=9.5−17.25=−7.759.5 + (-17.25) = 9.5 - 17.25 = -7.75

    The options provided are (a) 9, (b) 10, (c) 8. None of these match -7.75. Let me re-check the problem statement. It seems there might be a typo in the question or options. Assuming the calculation is correct based on the written expression.
    The simplified value is -7.75\boxed{\text{-7.75}}.

Part 26· 2 steps

Jide bought a textbook for N800 and later sold it to Effiom at a profit of 25%. Effiom sold it at a profit of 25% to Arieta. How much did Arieta bought the book from Effiom?

  1. Calculate the price Jide sold the book to Effiom.

    Jide's cost price = N800.
    Profit = 25% of N800 = 0.25×800=N2000.25 \times 800 = \text{N}200.
    Jide's selling price to Effiom = N800 + N200 = N1000.

  2. Calculate the price Effiom sold the book to Arieta.

    Effiom's cost price = N1000 (Jide's selling price).
    Profit = 25% of N1000 = 0.25×1000=N2500.25 \times 1000 = \text{N}250.
    Effiom's selling price to Arieta = N1000 + N250 = N1250.
    None of the options (a) N1300, (b) N1200, (c) N1100, (d) N1800 match the calculated value. I will provide the calculated answer.
    Arieta bought the book from Effiom for N1250\boxed{\text{N1250}}.

Part 27· 2 steps

A man is on a 2 hours journey, he starts the journey by 8:30 a.m. When will he end his journey?

  1. Add the duration of the journey to the start time.

    Start time = 8:30 a.m.
    Journey duration = 2 hours.

  2. Calculate the end time.

    8:30 a.m. + 2 hours = 10:30 a.m.
    The correct option is (d).
    He will end his journey at 10:30 a.m.\boxed{\text{10:30 a.m.}}.

Part 28· 2 steps

In a class of 40 pupils, 30% of them like rice. How many pupils do not like rice?

  1. Calculate the percentage of pupils who do not like rice.

    Total percentage = 100%.
    Percentage who like rice = 30%.
    Percentage who do not like rice = 100%−30%=70%100\% - 30\% = 70\%.

  2. Calculate the number of pupils who do not like rice.

    Number of pupils who do not like rice = 70% of 40.

    0.70×40=280.70 \times 40 = 28

    The correct option is (c).
    28 pupils\boxed{\text{28 pupils}} do not like rice.

Part 29· 2 steps

How many days are there in the months of January, April, September, and December?

  1. List the number of days for each specified month.

    • January: 31 days
    • April: 30 days
    • September: 30 days
    • December: 31 days
  2. Sum the number of days.

    31+30+30+31=122 days31 + 30 + 30 + 31 = 122\, \text{days}

    None of the options (a) 143 days, (b) 183 days, (c) 153 days match the calculated value. I will provide the calculated answer.
    There are 122 days\boxed{\text{122 days}} in the months of January, April, September, and December.

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