We read your photo as:

Write the formula for the volume of a sphere.

Mathematics

ScanSolve AI Answer

Step-by-step solution

13 steps

1. The volume of a spherical ball is 5,000 cm35,000 \text{ cm}^3. What is the radius of the ball correct to one decimal place? (Use π=3.14\pi = 3.14)

  1. Write the formula for the volume of a sphere.

    V=43πr3V = \frac{4}{3}\pi r^3

  2. Substitute the given values into the formula.

    5000=43×3.14×r35000 = \frac{4}{3} \times 3.14 \times r^3

  3. Isolate r3r^3.

    r3=5000×34×3.14r^3 = \frac{5000 \times 3}{4 \times 3.14} r3=1500012.56r^3 = \frac{15000}{12.56} r3≈1194.2675r^3 \approx 1194.2675

  4. Calculate rr by taking the cube root.

    r=1194.26753r = \sqrt[3]{1194.2675} r≈10.610 cmr \approx 10.610 \text{ cm}

  5. Round the radius to one decimal place.

    r≈10.6 cmr \approx 10.6 \text{ cm}

    The radius of the ball is 10.6 cm\boxed{\text{10.6 cm}}.

    2. A cone has a diameter of 70 mm70 \text{ mm} and a height of 100 mm100 \text{ mm}. What is its volume to the nearest mm3\text{mm}^3? (Use π=3.14\pi = 3.14)

  6. Calculate the radius from the given diameter.

    r=diameter2=70 mm2=35 mmr = \frac{\text{diameter}}{2} = \frac{70 \text{ mm}}{2} = 35 \text{ mm}

  7. Write the formula for the volume of a cone.

    V=13πr2hV = \frac{1}{3}\pi r^2 h

  8. Substitute the given values into the formula.

    V=13×3.14×(35 mm)2×100 mmV = \frac{1}{3} \times 3.14 \times (35 \text{ mm})^2 \times 100 \text{ mm} V=13×3.14×1225 mm2×100 mmV = \frac{1}{3} \times 3.14 \times 1225 \text{ mm}^2 \times 100 \text{ mm} V=13×384650 mm3V = \frac{1}{3} \times 384650 \text{ mm}^3 V≈128216.666... mm3V \approx 128216.666... \text{ mm}^3

  9. Round the volume to the nearest mm3\text{mm}^3.

    V≈128217 mm3V \approx 128217 \text{ mm}^3

    The volume of the cone is 128217 mm3\boxed{\text{128217 mm}^3}.

    3. Find the surface area of a box with dimensions 125 mm×64 mm×84 mm125 \text{ mm} \times 64 \text{ mm} \times 84 \text{ mm} to the nearest mm2\text{mm}^2.

  10. Identify the dimensions of the box.

    Length l=125 mml = 125 \text{ mm}
    Width w=64 mmw = 64 \text{ mm}
    Height h=84 mmh = 84 \text{ mm}

  11. Write the formula for the surface area of a rectangular box (cuboid).

    SA=2(lw+lh+wh)SA = 2(lw + lh + wh)

  12. Substitute the dimensions into the formula.

    SA=2((125 mm×64 mm)+(125 mm×84 mm)+(64 mm×84 mm))SA = 2((125 \text{ mm} \times 64 \text{ mm}) + (125 \text{ mm} \times 84 \text{ mm}) + (64 \text{ mm} \times 84 \text{ mm})) SA=2(8000 mm2+10500 mm2+5376 mm2)SA = 2(8000 \text{ mm}^2 + 10500 \text{ mm}^2 + 5376 \text{ mm}^2) SA=2(23876 mm2)SA = 2(23876 \text{ mm}^2) SA=47752 mm2SA = 47752 \text{ mm}^2

  13. The surface area is already an integer, so no rounding is needed to the nearest mm2\text{mm}^2.

    The surface area of the box is 47752 mm2\boxed{\text{47752 mm}^2}.

Was this helpful?

Still stuck on this one?

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

Got a different question?Ask your own question

More Mathematics Questions

QWhat is the formular for volume of a sphereQVolume of a sphere.QFind the surface area of the sphere.QWhat is the formula for volume of a coneQQuestion 2: The volume of a sphere is 38808 cm3. Find the radius. Use pi = 22/7.
Browse by topic:Geometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
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