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A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?

Mathematics

ScanSolve AI Answer

Answer

Volume

1980 cm3\text{1980 cm}^3

Lateral Surface Area

510 cm2\text{510 cm}^2

Total Surface Area

1038 cm2\text{1038 cm}^2

Step-by-step solution

3 steps
  1. Calculate the Volume of the cuboid.

    The dimensions are:
    Length (ll) = 22 cm
    Breadth (bb) = 12 cm
    Height (hh) = 7.5 cm

    The formula for the volume of a cuboid is V=l×b×hV = l \times b \times h.

    V=22 cm×12 cm×7.5 cmV = 22 \text{ cm} \times 12 \text{ cm} \times 7.5 \text{ cm} V=264 cm2×7.5 cmV = 264 \text{ cm}^2 \times 7.5 \text{ cm} V=1980 cm3V = 1980 \text{ cm}^3
  2. Calculate the Lateral Surface Area (LSA) of the cuboid.

    The formula for the lateral surface area of a cuboid is LSA=2h(l+b)\text{LSA} = 2h(l+b).

    LSA=2×7.5 cm×(22 cm+12 cm)\text{LSA} = 2 \times 7.5 \text{ cm} \times (22 \text{ cm} + 12 \text{ cm}) LSA=15 cm×(34 cm)\text{LSA} = 15 \text{ cm} \times (34 \text{ cm}) LSA=510 cm2\text{LSA} = 510 \text{ cm}^2
  3. Calculate the Total Surface Area (TSA) of the cuboid.

    The formula for the total surface area of a cuboid is TSA=2(lb+bh+hl)\text{TSA} = 2(lb + bh + hl).

    TSA=2((22 cm×12 cm)+(12 cm×7.5 cm)+(7.5 cm×22 cm))\text{TSA} = 2((22 \text{ cm} \times 12 \text{ cm}) + (12 \text{ cm} \times 7.5 \text{ cm}) + (7.5 \text{ cm} \times 22 \text{ cm})) TSA=2(264 cm2+90 cm2+165 cm2)\text{TSA} = 2(264 \text{ cm}^2 + 90 \text{ cm}^2 + 165 \text{ cm}^2) TSA=2(519 cm2)\text{TSA} = 2(519 \text{ cm}^2) TSA=1038 cm2\text{TSA} = 1038 \text{ cm}^2

    The volume, lateral surface area, and total surface area for the given dimensions are:
    Volume: 1980 cm3\boxed{\text{1980 cm}^3}
    Lateral Surface Area: 510 cm2\boxed{\text{510 cm}^2}
    Total Surface Area: 1038 cm2\boxed{\text{1038 cm}^2}

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