A cereal company wants to switch from a rectangular prism box to another type of box with about the same volume and less surface area. Which box would you recommend? Objectives: Define and recognize the relevance of nets in geometry, and construct and visualize nets. Calculate the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composite solids and their real-life applications. Use the appropriate formula to solve problems involving the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composite solids and their real-life applications. Product to be submitted You will submit proposals for each of 4 different types of cereal boxes (triangular prism, cylinder, cone, and square pyramid), along with your recommendation and explanation for which one the company should choose. A worksheet is provided for you to help organize your information. You can access the worksheet in the "Assignment Resources" section below. Instructions The Sweet Circles Cereal is currently sold in a rectangular prism box with the dimensions shown: Height=12in Length=8i eng in The owner of the company wants to go in a bold new direction and change the type of cereal box they use. Here are their guidelines: The new box can be in the shape of a triangular prism, cone, cylinder, or square pyramid. e The volume needs to remain about the same (within 10 cubic inches, more or less). To save the company some money, the surface area of the new box needs to be less than or equal to the surface area of the current box (in order to have less cost to make the box). You will use these guidelines to come up with proposals for each of the boxes mentioned (a triangular prism box, cone box, cylinder box, and square pyramid box) with a sketch of the box and the box's net. Find and compare the surface areas and volumes (be sure to show your work). Then you will provide your recommendation as to which box the company should choose and why. Volume (within Surface Area Dimensions 3-D box view with Net view 10 cubic inches Box Shape (less than or equal to measurements more or less 272 square inches) of 192 cubic inches) Sweet Circles Height = 12 in SA = 2(1w) + 2(1h) + 2(wh) V = lwh L = 8 in Rectangular prism (original Cereal W = 2 in box) SA = 2(8*2) + 2(8*12) + 2(2*12) = 272 square V = 8*2*12 = 192 cubic H = 12 in inches inches Length = 8 in Width = 2 in Triangular Prism Cone Cylinder Square Pyramid