We read your photo as:

Calculate the volume of water in a cylindrical dam that is 80% full, given outer diameter, wall thickness, height, and percentage full.

Mathematics

ScanSolve AI Answer

Answers

2 parts
1.1

30.000 kl\text{30.000 kl}

1.2

4.5 cm\text{4.5 cm}

Step-by-step solution

9 steps

Here are the solutions to your questions.

Part 1.1· 6 steps

  1. Convert the wall thickness from centimeters to meters.

    35 cm=0.35 m35 \text{ cm} = 0.35 \text{ m}
  2. Calculate the inner diameter of the dam.

    The outer diameter is 6 m, and the wall thickness is 0.35 m on each side.

    Inner diameter=Outer diameter−2×Wall thickness\text{Inner diameter} = \text{Outer diameter} - 2 \times \text{Wall thickness} Inner diameter=6 m−2×0.35 m\text{Inner diameter} = 6 \text{ m} - 2 \times 0.35 \text{ m} Inner diameter=6 m−0.70 m\text{Inner diameter} = 6 \text{ m} - 0.70 \text{ m} Inner diameter=5.3 m\text{Inner diameter} = 5.3 \text{ m}
  3. Calculate the inner radius of the dam.

    Inner radius(r)=Inner diameter2\text{Inner radius} (r) = \frac{\text{Inner diameter}}{2} r=5.3 m2r = \frac{5.3 \text{ m}}{2} r=2.65 mr = 2.65 \text{ m}
  4. Calculate the full volume of the dam's interior (the space for water).

    The dam is a cylinder with height h=1.7 mh = 1.7 \text{ m}.

    Volume of cylinder=πr2h\text{Volume of cylinder} = \pi r^2 h Volumefull=π×(2.65 m)2×1.7 m\text{Volume}_{full} = \pi \times (2.65 \text{ m})^2 \times 1.7 \text{ m} Volumefull=π×7.0225 m2×1.7 m\text{Volume}_{full} = \pi \times 7.0225 \text{ m}^2 \times 1.7 \text{ m} Volumefull≈3.14159×7.0225×1.7 m3\text{Volume}_{full} \approx 3.14159 \times 7.0225 \times 1.7 \text{ m}^3 Volumefull≈37.500 m3\text{Volume}_{full} \approx 37.500 \text{ m}^3
  5. Calculate the volume of water when the dam is 80% full.

    Volumewater=0.80×Volumefull\text{Volume}_{water} = 0.80 \times \text{Volume}_{full} Volumewater=0.80×37.500 m3\text{Volume}_{water} = 0.80 \times 37.500 \text{ m}^3 Volumewater=30.000 m3\text{Volume}_{water} = 30.000 \text{ m}^3
  6. Convert the volume of water to kilolitres.

    Given that 1 m3=1 kl1 \text{ m}^3 = 1 \text{ kl}.

    Volumewater=30.000 kl\text{Volume}_{water} = 30.000 \text{ kl}

    The volume of water in the dam is 30.000 kl\boxed{\text{30.000 kl}}.

Part 1.2

4.5 cm\text{4.5 cm}

  1. Convert the area from square millimeters to square centimeters to match the height unit.

    Given height h=8 cmh = 8 \text{ cm}.
    Given area A=1800 mm2A = 1800 \text{ mm}^2.
    Since 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}, then 1 cm2=(10 mm)2=100 mm21 \text{ cm}^2 = (10 \text{ mm})^2 = 100 \text{ mm}^2.

    A=1800 mm2100 mm2/cm2A = \frac{1800 \text{ mm}^2}{100 \text{ mm}^2/\text{cm}^2} A=18 cm2A = 18 \text{ cm}^2
  2. Use the formula for the area of a triangle to find the base length.

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} 18 cm2=12×base×8 cm18 \text{ cm}^2 = \frac{1}{2} \times \text{base} \times 8 \text{ cm}
  3. Solve for the base length.

    18 cm2=4 cm×base18 \text{ cm}^2 = 4 \text{ cm} \times \text{base} base=18 cm24 cm\text{base} = \frac{18 \text{ cm}^2}{4 \text{ cm}} base=4.5 cm\text{base} = 4.5 \text{ cm}

    The base length of the triangle is 4.5 cm\boxed{\text{4.5 cm}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp