Question

The figure is made up of a cylinder, a cone, and a half sphere. The radius of the half sphere is 3 inches. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder, half sphere, and cone. The radius for all figures is 3 inches. The height of the cylinder is 6 inches and height of the cone is 4 inches. Recall the formulas V = B h V = one-third B h and V = four-thirds pi r cubed

Answer 1

The volume of the composite figure is 263.76 inches³

Step-by-step explanation:

The volume of a cylinder of radius r and height h is

• V = πr²h ⇒ Bh

The volume of a cone of radius r and height h is

• V = $\frac{1}{3}$ πr²h ⇒ $\frac{1}{3}$ Bh

The volume of a sphere with radius r is

• V = $\frac{4}{3}$ πr³

∵ The figure is made up of a cylinder, a cone, and a half sphere

∵ The radius of the cylinder = 3 inches

∵ The height of the cylinder = 6 inches

∵ π = 3.14

- Use the rule of the volume of the cylinder above

∴ The volume of the cylinder = (3.14)(3)²(6)

∴ The volume of the cylinder = 169.56 inches³

∵ The radius of the cone = 3 inches

∵ The height of the cone = 4 inches

∵ π = 3.14

- Use the rule of the volume of the cone above

∴ The volume of the cone = $\frac{1}{3}(3.14)(3)^{2}(4)$

∴ The volume of the cone = 37.68 inches³

∵ The radius of the half sphere = 3 inches

∵ π = 3.14

- Use the rule of the volume of the sphere above to find the

   volume of the half sphere

∴ The volume of half sphere = $(\frac{1}{2})(\frac{4}{3})(3.14)(3)^{3}$

∴ The volume of half sphere = 56.52 inches³

To find the volume of the composite figure add the volumes of the three shapes above

∵ The volume of the composite figure = 169.56 + 37.68 + 56.52

∴ The volume of the composite figure = 263.76 inches³

The volume of the composite figure is 263.76 inches³

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Answer 2

Answer:

263.76 inches³

Step-by-step explanation:

just did on EDG 2020