2. If the total surface area of a sphere is 154 cm2. Find its total volume.

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Problem: Finding the Volume of a Sphere Given Data: Total surface area of the sphere: 154 cm² Solution Steps: Find the Radius of the Sphere: The formula for the surface area of a sphere is 4πr24πr2, where rr is the radius. Given 4πr2=1544πr2=154 cm², we solve for rr. Calculate...
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Problem: Finding the Volume of a Sphere Given Data: Total surface area of the sphere: 154 cm² Solution Steps: Find the Radius of the Sphere: The formula for the surface area of a sphere is 4πr24πr2, where rr is the radius. Given 4πr2=1544πr2=154 cm², we solve for rr. Calculate the Volume of the Sphere: Once we find the radius, we can use the formula for the volume of a sphere, 43πr334πr3, to find the volume. Detailed Solution: Finding the Radius of the Sphere: Surface area formula: 4πr2=1544πr2=154 cm² Solving for rr: r2=1544πr2=4π154 r2=1544×3.14r2=4×3.14154 (Using ππ approximately as 3.14) r2≈15412.56r2≈12.56154 r2≈12.27r2≈12.27 r≈12.27r≈12.27 r≈3.5r≈3.5 cm (approximated to one decimal place) Calculate the Volume of the Sphere: Using the radius r=3.5r=3.5 cm in the volume formula: Volume V=43πr3V=34πr3 V=43×3.14×(3.5)3V=34×3.14×(3.5)3 V≈43×3.14×42.875V≈34×3.14×42.875 V≈43×3.14×42.875V≈34×3.14×42.875 V≈43×3.14×42.875V≈34×3.14×42.875 V≈179.59V≈179.59 cm³ Conclusion: The total volume of the sphere is approximately 179.59179.59 cubic centimeters. read less
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