Honors Geometry 1-2 - Chapter 11
If 2 shapes are similar with a scale factor of a/b, then...
- lengths have a scale factor of a/b - areas have a scale factor of a^2/b^2 - volumes have a scale factor of a^3/b^3
Darren is hanging a picture frame that is shaped like a regular pentagon with outside lengths of 9 inches. What is the area this picture frame will take up on Darren's wall? Round your answer to the nearest tenth.
139.4 in^2
A pyramid has a height of 18 centimeters and a base with an area of 26 square centimeters. Find the volume.
156 cm^3
A metal pipe is shaped like a cylinder with a height of 50 inches and a radius of 6 inches. What is the exterior surface area of the pipe? Round your answer to the nearest tenth.
1885 in^2
A circular window on a ship is designed with a radius of 8 inches. What is the area of glass needed for the window? Round your answer to the nearest hundredth.
201.06 in^2
A trapezoid has base lengths of 12 and 14 feet and an area of 322 square feet. What is the height of the trapezoid to the nearest tenth of a foot?
24.8 ft
Find the area of the circle that contains the sector described below. Round to the nearest tenth, if necessary. One sector has an area of 210 square centimeters and an arc measure of 30°.
2520 cm^2
Find the radius of a circle with an area of 2827.4 square feet. Round to the nearest tenth.
30 ft
Moesha cuts a spherical orange in half along a great circle. The radius of the orange is 2 inches. Find the approximate volume of the orange to the nearest tenth of a cubic inch.
33.5 in^3
Margaret makes a square frame out of four pieces of wood. Each piece of wood is a rectangular prism with a length of 40 centimeters, a height of 4 centimeters, and a depth of 6 centimeters. What is the total volume of the wood used in the frame?
3840 cm^3
Spaceship Earth at Disney's Epcot Center is a sphere. If the circumference of Spaceship Earth is C=7πx², find the surface area in terms of x and π.
49 pi x^4
Area of a trapezoid
area = 1/2 * height (base1 + base2)
Area of a polygon
area = 1/2 base * height (# of sides)
Area of a kite/rhombus
area = 1/2 diagonal1 * diagonal2
Area of sectors
area = arc length/360 (pi * radius²)
Area of a rectangle/parallelogram
area = base * height
Area of a Circle
area = pi * radius²
Reshan rotated a semicircle about a vertical axis to create a sphere. Describe another way Reshan could have rotated a semicircle about an axis to generate a sphere. Reshan could have rotated the semicircle around a...
horizontal axis
Find the lateral area and surface area of a triangular prism with a height of 6 inches and a right triangular base with legs of 9 inches and 12 inches. Round to the nearest tenth, if necessary.
lateral area = 216 in^2 surface area = 324 in^2
Find the lateral area and surface area of a cone with a diameter of 3.4 centimeters and a slant height of 6.5 centimeters. Round to the nearest tenth, if necessary.
lateral area = 34.7 cm^2 surface area = 43.8 cm^2
Find the lateral area and surface area of a square pyramid with an altitude of 12 inches and a slant height of 18 inches. Round to the nearest tenth, if necessary.
lateral area = 966 in^2 surface area = 1686 in^2
Surface area of a pyramid
surface area = (1/2 perimeter * slant height) + (area of the base)
Surface are of a prism
surface area = (perimeter * height) + 2(area of the base)
Surface area of a cone
surface area = (pi * radius * slant height) + (pi * radius²)
Surface area of a cylinder
surface area = 2( pi * radius * height) + 2( pi * radius²)
Surface area of a sphere
surface area = 4 pi * radius²
Volume of a pyramid
volume = 1/3 area of base * height
Volume of a cone
volume = 1/3 pi * radius² * height
Volume of a sphere
volume = 4/3 pi * radius³
Volume of a prism
volume = area of base * height
Volume of a cylinder
volume = pi * radius² * height
The part of a dish designed for ice cream is shaped like a cone. The base of the cone has a radius of 2 inches and the height is 1.2 inches. What is the volume of the cone? Round your answer to the nearest hundredth.
5.03 in^3
A roasting company sells their coffee in canisters shaped like a cylinder. The radius of the canister is 1.5 inches and the height is 7.5 inches. What is the approximate volume of a coffee canister? Round your answer to the nearest cubic inch.
53 in^3
One diagonal of a kite is four times as long as the other diagonal. If the area of the kite is 72 square meters, what are the lengths of the diagonals?
6m; 24m
A cylinder has a lateral area of 120π square meters and a height of 7 meters. Find the radius of the cylinder. Round to the nearest tenth.
8.6 m