True or false. If the statement is true, provide an example with WORK shown. If the statement is false, provide a corrected statement.
a. If you triple the length and width of a rectangle then you triple its perimeter.
No matter the numbers you chose the answer to this statement should be True.
Perimeter formula: 2(L) + 2(w) or add up all the sides.
100
Find the circumference of a circle with a radius of 2cm?
Use the π key and not 3.14
C= 2πr
C= 2π(2)
C=4π
C= 12.6cm
200
If a circle has an area of 121π cm2, what is the diameter?
You have an extra large spherical balloon with radius 12 inches.
a. You let enough air out to reduce the radius to 6 inches. What happens to the volume compared to the original volume?
The scale factor is 1/2 being that spherical balloon went from 12 to 6.
Spheres are three dimensional shapes which means our scale factor has to be cubed.
(1/2)3= 1/8
The volume is 1/8 as big
200
Find the circumference of a circle that has a radius of 3.5yd. Use the π key in your calculator and not 3.14
C=2πr
C=2π(3.5)
C=7π
C= 21.99 =22yd
300
If you triple the length and width of a rectangle then you triple its area.
False
Remember: Area= L x W
300
What is the volume of a cone in terms of pi with the radius being 5cm and the height being 21cm.
v= 1/3π(r2)h
v= 1/3π(5^2)21
v=175π cm3
300
A block of wood 3 cm on each side has a mass of 27 g. What is the density of the block?
Density= Mass/Volume
Density= 27/x
Volume= L x W x H = 3 x 3 x 3 = 27
Density = 27/27 = 1gram
300
A large pizza has a diameter of 12 inches. A small pizza has a diameter of 6 inches.
a. What is the ratio of the diameters of the large pizza to the small pizza?
Big/Small = 12/6=2
The bigger pizza is two times as big as the smaller one
300
What is the circumference of a circle that has a radius of 28m?
Use the π key instead of 3.14
C = 2 π r
= 2 π (28 m)
= 56 π mi
400
What is the area of a circle that has a radius of 3.1m?
A= πr2
A= π(3.1)2
A= 9.6π
A= 30.2m2
400
A prism has a base with the area 30cm2. The height of the prism is 9cm. What is the volume of the prism?
V= BH
V= (30)(9)
v=270cm3
400
If the cube has a mass of 173 grams, and each side of the cube is 4 cm each what is its density?
Density= Mass/Volume
Density= 173/x
Volume= l x w x h = 4 x 4 x 4 = 64 cm3
Density= 173/64= 2.70 g/cm3
400
2) An inflatable sphere is inflated from a diameter of 10 inches to a diameter of 20 inches.
a. What is the ratio of surface areas of the inflated sphere to the original sphere?
Surface Area: 2^2=4
400
What is the circumference of a circle that has a diameter of 15 m?
Use the π key and not 3.14
(π)(diameter)
C= 47.12
500
What is the area of a circle that has a diameter of 10?
A= πr2
Radius is half of the diameter = 10/2=5
A=π(5)2
A= 25π
A= 78.5 m2
500
Find the volume of the cube with each side being 5 cm.
V=s3
V=(5)3= 125
500
New York City has 8.3 million people and an area of 1200 km2. Tokyo has 13.2 million people and an area of 2200 km2. Which city has a greater population density?
Population Density= Population/Area
New York Population Density= 8,300,000/1200km2= 6,916.7 km2
Tokyo Population Density= 13,200,000/2200km2= 6,000 km2
NEW YORK !
500
A sphere has a volume of 39π cubic centimeters. The sphere is freeze-dried, resulting in a reduction by 1/3 of the radius. What is the new volume? What is the ratio of the new volume to the old volume?
dimension=1/3
new scale factor=(1/3)3 = 1/27
new volume=39π(1/27)= 13π/9= 4.53cm3
500
What is the circumference of a circle that has a diameter of 6.6 in