. Ms. Johnson, a circus ringleader, made a cake in the shape of a circus tent to use as the centerpiece at a celebration. As sho
wn in the illustration, the cake consists of a cylinder and a cone. The height of the cone is one-half the height of the cylinder. The volume of the cylinder is 3 1470 in . The diameter of the cylinder is 12 in. What is the volume of the circus tent cake? Use 3.14 for . Round to the nearest hundredth. Ms. Johnson wants all the circus employees to have miniature cakes in the shape of either a circus ball or a
clown hat. She wants the clown hat dessert and the circus ball dessert to have equal volumes. The radius of
both cake pieces will be 3 in. What must the height of the clown hat cake be for the two cakes to be equal in
volume? Round to the nearest hundredth if necessary. Explain or show your work.
The formula for the volume of a cylinder is V=πr²h. Substituting the information we have, we get 1470=(3.14)(6²)<span>h </span>1470=113.04h Divide both sides by 113.04: 1470/113.04 = 113.04h/113.04 13 ≈ h The height of the cylinder is 13 inches. We know that the height of the cone is 1/2 the height of the cylinder; 1/2(13) = 6.5 inches. The formula for the volume of a cone is: V=1/3πr²h The cone and the cylinder have the same radius, and we now know that the height of the cone is 6.5. Substituting this information in we have: V=1/3(3.14)(6²)(6.5) = 244.92 in³ The total volume of the cake would be the volume of the cylinder added to the volume of the cone: 1470+244.92 = 1714.92 in³.
The formula for the volume of a sphere, for the ball cake, is <em /><em>V</em>=4/3πr³. Using the radius of 3 we have: <span><em>V</em>=4/3(3.14)(3</span>³)=113.04 for the volume of the circus ball cake. The formula for the area of the cone-shaped hat cake is <em>V</em>=1/3π<em>r</em>²<em>h</em>. We want it to have the same volume as the circus ball cake, and we know the radius is still 3: <em />113.04=1/3(3.14)(3²)<em>h</em> This simplifies to 113.04=9.42<em>h</em> Divide both sides by 9.42: 113.04/9.42 = 9.42<em>h</em>/9.42 The hat cake would have to have a height of 12 inches to have the same volume.
