A cyndrical solid of diameter 56cm has a circular hole of radius 7 cm and alength 120cm what is the volume of the solid?,what is the density of the solid if it weighs 50g?

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Answers

2 parts
1

277200 cm3277200 \text{ cm}^3

2

0.0001804 g/cm30.0001804 \text{ g/cm}^3

Step-by-step solution

7 steps

Here's how to calculate the volume and density of the solid:

Part 1· 4 steps

Volume of the solid

The solid is a cylinder with a circular hole, so its volume is the volume of the outer cylinder minus the volume of the inner hole.

  1. Identify the dimensions.

    • Diameter of the solid = 56 cm56 \text{ cm}, so the radius of the outer cylinder (RR) = 562=28 cm\frac{56}{2} = 28 \text{ cm}.
    • Radius of the circular hole (rr) = 7 cm7 \text{ cm}.
    • Length (height) of the solid (hh) = 120 cm120 \text{ cm}.

  2. Calculate the volume of the outer cylinder.

    Vouter=πR2h=π(28 cm)2(120 cm)V_{outer} = \pi R^2 h = \pi (28 \text{ cm})^2 (120 \text{ cm})

  3. Calculate the volume of the inner hole.

    Vinner=πr2h=π(7 cm)2(120 cm)V_{inner} = \pi r^2 h = \pi (7 \text{ cm})^2 (120 \text{ cm})

  4. Calculate the volume of the solid.

    Vsolid=Vouter−Vinner=πR2h−πr2h=πh(R2−r2)V_{solid} = V_{outer} - V_{inner} = \pi R^2 h - \pi r^2 h = \pi h (R^2 - r^2)

    Using π=227\pi = \frac{22}{7}:

    Vsolid=227×120 cm×((28 cm)2−(7 cm)2)V_{solid} = \frac{22}{7} \times 120 \text{ cm} \times ((28 \text{ cm})^2 - (7 \text{ cm})^2) Vsolid=227×120 cm×(784 cm2−49 cm2)V_{solid} = \frac{22}{7} \times 120 \text{ cm} \times (784 \text{ cm}^2 - 49 \text{ cm}^2) Vsolid=227×120 cm×735 cm2V_{solid} = \frac{22}{7} \times 120 \text{ cm} \times 735 \text{ cm}^2 Vsolid=22×120 cm×7357 cm2V_{solid} = 22 \times 120 \text{ cm} \times \frac{735}{7} \text{ cm}^2 Vsolid=22×120 cm×105 cm2V_{solid} = 22 \times 120 \text{ cm} \times 105 \text{ cm}^2 Vsolid=2640 cm×105 cm2V_{solid} = 2640 \text{ cm} \times 105 \text{ cm}^2 Vsolid=277200 cm3V_{solid} = 277200 \text{ cm}^3

    The volume of the solid is 277200 cm3\boxed{277200 \text{ cm}^3}.

Part 2

0.0001804 g/cm30.0001804 \text{ g/cm}^3

Density of the solid

  1. State the given mass and the calculated volume.

    • Mass (mm) = 50 g50 \text{ g}
    • Volume (VV) = 277200 cm3277200 \text{ cm}^3

  2. Use the formula for density, ρ=mV\rho = \frac{m}{V}.

    ρ=50 g277200 cm3\rho = \frac{50 \text{ g}}{277200 \text{ cm}^3} ρ=527720 g/cm3\rho = \frac{5}{27720} \text{ g/cm}^3 ρ≈0.000180375 g/cm3\rho \approx 0.000180375 \text{ g/cm}^3

  3. Round the density to a suitable number of significant figures (e.g., four significant figures).

    ρ≈0.0001804 g/cm3\rho \approx 0.0001804 \text{ g/cm}^3

    The density of the solid is 0.0001804 g/cm3\boxed{0.0001804 \text{ g/cm}^3}.

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