GLEN-GEOMETRY 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.
ANS: V(x) = 2x(12.5 - 2x)(17 - 2x)
B. What are the dimensions of each of the eight squares that should be
removed to produce a box with maximum volume?
ANS: 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.
ANS: r = 1 in., h = 5 in
- Esteban is preparing to start an ice sculpture.He wants to reduce the volume of the ice to 3/5 of the original volume. How much should he take from each dimension?
ANS: about 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.
ANS: 9 cm
- The It’s A Snap Puzzle Company is designing new boxes for their 2000
piece 3-D puzzles…
A. Write a polynomial function that models the volume of the new box.
ANS: 𝑉(𝑥) = 𝑥³ + 60𝑥⅖+ 1025𝑥 + 3750
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 = 𝑥³ + 60𝑥² + 1025𝑥 + 3750
C. Find the dimensions of the new box.
ANS: about 26.7 cm by 31.7 cm by 6.7 cm
- Suppose the light pattern from a fog light can be modeled by the equation
𝑥²/25−𝑦²/= 1. Find the coordinates of three additional
points on the graph and the other x-intercept.
ANS: (5,0)
- Radio waves emitted from two different radio towers interfere with each
other’s signal. At what coordinates might Juana live relative to the midpoint between
the two towers?
ANS: (4 sqrt 2, 6) or ( -4 sqrt 2, 6)
- The Band Boosters at Palermo High School are having their annual doughnut sale to raise money for new equipment. What is the p-intercept of the line represented by this equation?
ANS: - 250
- Domingo decides to ride the Ferris wheel at the local carnival. When he gets into the seat that is at the bottom of the Ferris wheel, he is 4 feet above the
ground.
A. If the radius of the Ferris wheel is 36 feet, how far above the ground will
Domingo be when his seat reaches the top?
ANS: 76 ft
B. The Ferris wheel rotates 300° counterclockwise and stops to let another
passenger on the ride. How far above the ground is Domingo when the Ferris
wheel stops?
ANS: 22 ft
C. Suppose the radius of the Ferris wheel is only 30 feet. How far above the
ground is Domingo after the Ferris wheel rotates 300°?
ANS: 19 ft
D. Suppose the radius of the Ferris wheel is r. Write an expression for the
distance from the ground to Domingo after the Ferris wheel rotates 300°.
ANS: ½ r + 4
