Geometry edited Flashcards
A 12.5 centimeter by 34 centimeter piece of cardboard will have eight
congruent squares removed as in the diagram. The box will be folded to create a take-out hamburger box
A. Find the model for the volume V(x) of the box as a function of the length x of the sides of the eight squares removed.
V(x) = 2x(12.5 - 2x)(17 - 2x)
A 12.5 centimeter by 34 centimeter piece of cardboard will have eight
congruent squares removed as in the diagram. The box will be folded to create a take-out hamburger box
B. What are the dimensions of each of the eight squares that should be
removed to produce a box with maximum volume?
2.37 cm by 2.37 cm
A cylinder has a height 4 inches greater than the radius of its base. Find the radius and the height to the nearest inch if the volume of the cylinder is 5 cubic inches.
r = 1 in., h = 5 in
Esteban is preparing to start an ice sculpture. He has a block of ice that is 3 feet by 4 feet by 5 feet. Before he starts, he wants to reduce the volume of the ice by shaving off the same amount from the length, the width, and the height.
οΏ½
οΏ½(π₯) = βπ₯3+12π₯2β47π₯ +60
He wants to reduce the volume of the i
0.60 ft
A cone is inscribed in a sphere with a radius of 15 centimeters. If the volume of the cone is 1152 cubic centimeters, find the length represented by x.
9cm
- The Itβs A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.
A. Write a polynomial function that models the volume of the new box.
ANS: π(π₯) = π₯3 + 60π₯2+1025π₯ +3750
ANS: π(π₯) = π₯3 + 60π₯2+1025π₯ +3750
- The Itβs A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.
B. The volume of the new box must be 1.5 times the volume of the old box to hold the increase in puzzle pieces. Write an equation that models this situation.
ANS: 5625 = π₯3+60π₯2+1025π₯ +3750
- The Itβs A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.
C. Find the dimensions of the new box.
ANS: about 26.7 cm by 31.7 cm by 6.7 cm
