01 C = 10π inches; A = 25π square inches
Step-by-step explanation:
01) Since the Circumference formula and Circle area formula is given by the following formulas we have:
D= 2r D =10'' then R=5''
![C=2\pi r\: C=2\pi*5''\, \: C=10\pi''](/tpl/images/0286/2978/5ce75.png)
Circle Area
![C=\pi r^{2}\: C=\pi5^{2}\, C=25\pi''](/tpl/images/0286/2978/e7884.png)
02) The Volume of a Cylinder is given by calculating the Base Area times the Height.
D=2R 6 then Radius is equal to 3. h=3R h=9
![V=Base_{area}*height\: V=\pi r^{2}*h\\V=3.14*3^{2}*9\: \: V=254.34](/tpl/images/0286/2978/2fab2.png)
254.34 cubic inches.
03) The volume of a cone is 1/3 of the volume of a cylinder.
Then the volume of the soda can (cylinder) is 36. And the Diameter is twice the Radius.
Firstly let's find out the height of the cylinder (soda can)
![V=\pi*r^{2}*h \\36=3.14*2^{2}*h \mapsto h=\frac{36}{12.56}\therefore h=2.86\\\\h=2.86 u](/tpl/images/0286/2978/0d3f9.png)
The Volume of Cone is one third of the Cylinder volume.
![\\V_{cone}=\frac{1}{3}\pi r^{2}*h\\V_{cone}=\frac{1}{3}*3.14* r^{2}*2.86\\V_{cone}=\frac{1}{3}3.14* 2^{2}*2.86\\V_{cone}=11.97\approx 12 u^{3}](/tpl/images/0286/2978/1479a.png)
4)
Missing picture.
5)
Similarly to the Cylinder and the Cone, the Prism and the Pyramid has the 1/3 proportion when it comes to Volume relation.
So the Volume of cube a kind of prism.
![V=a^{3}\, 36=a^{3}\, a=\sqrt[3]{36} \, a=3.30\\V_{pyramid}=\frac{1}{3}(\sqrt[3]{36})^{2}*(\sqrt[3]{36})\\\, V_{pyramid}=12](/tpl/images/0286/2978/7e252.png)
![Iwill give 5 stars question 1 (multiple choice worth 4 points) (08.01 lc) find the circumference and](/tpl/images/0286/2978/85235.jpg)
![Iwill give 5 stars question 1 (multiple choice worth 4 points) (08.01 lc) find the circumference and](/tpl/images/0286/2978/0b2f5.jpg)
![Iwill give 5 stars question 1 (multiple choice worth 4 points) (08.01 lc) find the circumference and](/tpl/images/0286/2978/ff412.jpg)