Question

An ice cream cone has a height of 6 inches and a radius of 2 inches as shown. The ice cream completely fills the cone, as well as the half-sphere above the cone. Find the total volume of ice cream, in cubic inches. Justify your answer. Round to the nearest hundredth.

Answer 1

the cone itself is 25.13, with the half sphere added it’s 41.8 :)

Answer 2

Volume of the ice cream in the cone will be 81.68 cubic inches.

   Given in the question,

• An ice cream cone with the height of 6 inches and radius of 2 inches.

• If the ice completely fills the cone, it takes the shape of the cone as ell as hemisphere above the cone.

By these conditions,

Volume of the ice cream in the cone = Volume of the cone + Volume of the hemisphere

Since, volume of the cone = $\frac{1}{3}\pi r^{2}h$

                                            = $\frac{1}{3}\pi (2)^{2}(6)$

                                            = $8\pi$ cubic inches

Volume of the hemisphere = $\frac{2}{3}\pi (3)^{3}$

                                             = $18\pi$ cubic inches

Total volume = $(8\pi +18\pi )$ cubic inches

                      = $26\pi$

                      = 81.681

                      ≈ 81.68 cubic inches

  Therefore, volume of the ice cream will be 81.68 cubic inches.

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