Answers
Set 81
- x= 6 feet.The radius of cylinder P is represented by x; it is the
only missing variable in the volume formula. Plug it in and solve
for x: 432πcubic ft. = (πx^2 )12 ft. 36 sq. ft. = x^2. 6 feet = x. - Surface area= 216πsquare feet.The surface area of a cylinder is
2 πr^2 + 2πrh: Plug the variables in and solve: SA = 2π(6 ft)^2 + 2π(6
ft. ×12 ft.). 72πsq. ft.+ 144πsq. ft. = 216πsq. ft. - Total volume= 864πcubic feet.This problem is easier than
you think. Each cone has exactly the same volume. The three
cones together equal the volume of the cylinder because a cone
has ^13 the volume of a cylinder with the same height and radius.
Multiply the volume of the cylinder by 2, and you have the
combined volume of all three cones and the cylinder.
Set 82
- x= ^12 inch. The formula for volume of a sphere is πr^3. In this
question xis the value of r. Plug the variables in and solve for x:
^16 π= πx^3. ^16 = x^3. ^12 = x. - y= ^14 inch.The volume of a cone is ^13 πr^2 h, where yis the value of
r. Plug in the variables and solve: 916 πcubic in. = ^13 πy^2 ^12 in. 916 π
cubic in. = ^16 πy^2. 116 πsq. in. = y^2. ^14 inch = y. - Surface area= 1.0πsquare inch.The candy inside the wrapper is
a perfect sphere. The formula for its surface area is 4πr^2. Plug the
variables in and solve: SA = 4π(0.5 inch)^2. SA= 1.0πsquare inch.
Set 83
- Jarret.The volume of a half sphere is ^12 (^43 πr^3 ). Tracy’s half scoop is
then ^12 (^43 π×1 inch^3 ), or ^23 πcubic inches. The volume of a cone is
^13 πr^2 h. The ice cream in the cone is ^13 π(1 inch^2 ×3 inches), or π
cubic inches. Jarret has ^13 πcubic inches more ice cream than Tracy.
501 Geometry Questions