Respuesta :
Answer:
Part 1) The surface area of the prism is equal to [tex]202\ m^{2}[/tex]
Part 2) The surface area of the cylinder is equal to [tex]412.0\ cm^{2}[/tex]
Part 3) The surface area of Tyson's cereal box is [tex]404\ in^{2}[/tex]
part 4) The volume of rectangular prism is [tex]12\ m^{3}[/tex]
Part 5) The prism's height is [tex]3\ cm[/tex]
Part 6) The shape of the newly-exposed section is a triangle
Part 7)
Part a) The surface area of cylinder is [tex]384.7\ ft^{2}[/tex]
Part b) The volume of cylinder is [tex]538.5\ ft^{3}[/tex]
Step-by-step explanation:
Part 1)
The surface area of the prism is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Find the area of the base B
[tex]B=LW=4*5=20\ m^{2}[/tex]
Find the perimeter of the base P
[tex]P=2(L+W)=2(4+5)=18\ m[/tex]
[tex]h=9\ m[/tex]
Find the surface area
[tex]SA=2B+Ph[/tex] ----> [tex]SA=2(20)+18(9)=202\ m^{2}[/tex]
Part 2)
The surface area of the cylinder is equal to
[tex]SA=2\pi r^{2} +2\pi r(h)[/tex]
we have
[tex]r=4\ cm[/tex]
[tex]h=12.4\ cm[/tex]
Find the surface area
assume [tex]\pi =3.14[/tex]
[tex]SA=2\pi (4^{2}) +2\pi (4)(12.4)=131.2\pi=412.0\ cm^{2}[/tex]
Part 3) we know that
The surface area of Tyson's cereal box is equal to area of the top and the bottom plus the area of the sides plus the area of the front and the back of the box
so
Area of the top and the bottom
[tex]A=2(11*8)=176\ in^{2}[/tex]
Area of the sides
[tex]A=2(11*6)=132\ in^{2}[/tex]
Area of the front and the back
[tex]A=2(8*6)=96\ in^{2}[/tex]
The surface area is equal to
[tex]SA=176+132+96=404\ in^{2}[/tex]
Part 4) we know that
The volume of rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=4*3*1=12\ m^{3}[/tex]
Part 5) we know that
The volume of rectangular prism is equal to
[tex]V=LWH[/tex]
solve for H
[tex]H=V/(LW)[/tex]
substitute the values
[tex]H=120/(5*8)=3\ cm[/tex]
Part 6) we know that
if you cut a square pyramid in half using a single cut, then the shape of the newly-exposed section is a triangle
Part 7)
Part a) we know that
The surface area of the cylinder is equal to
[tex]SA=2\pi r^{2} +2\pi r(h)[/tex]
we have
[tex]r=3.5\ ft[/tex]
[tex]h=14\ ft[/tex]
Find the surface area
assume [tex]\pi =3.14[/tex]
substitute
[tex]SA=2\pi (3.5^{2}) +2\pi (3.5*14)=122.5\pi=384.7\ ft^{2}[/tex]
Part b) we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=3.5\ ft[/tex]
[tex]h=14\ ft[/tex]
assume [tex]\pi =3.14[/tex]
substitute the values
[tex]V=\pi (3.5^{2})(14)=171.5\pi=538.5\ ft^{3}[/tex]
Answer:
1. Surface Area of Prism = 426 [tex]\,m^2[/tex]
2. Surface Area of Cylinder = [tex]181.0 \:cm^2[/tex]
3. Surface Area of Cereal Box = 404 [tex]\,inch^2[/tex]
4. Volume of Rectangular Prism = 12 [tex]m^3[/tex]
5. Height of Prism = 30 cm
6. The Shape of Newly exposed section is Triangle.
7. Surface Area of Cylinder = [tex]385 \:ft^2[/tex]
Volume of Cylinder = [tex]539 \:ft^3[/tex]
Step-by-step explanation:
Part 1.
Given dimensions are of prism with rectangle base i.e., Cuboid.
Length = 12 m, Width = 5 m, Height = 9 m
Surface Area of Prism = Total Surface Area of Cuboid
= 2(Length × Width + Width × Height + Height × Length)
= 2(12 × 5 + 5 × 9 + 9 × 12)
= 2(60 + 45 + 108)
= 2 × 213
= 426 [tex]\,m^2[/tex]
Surface Area of Prism = 426 [tex]\,m^2[/tex]
Part 2.
Given Dimension of cylinder are length or diameter = 4 cm and Height, h = 12.4 cm
radius, r = [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{4}{2}[/tex] = 2 cm
Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]
= [tex] 2\pi \times2\times12.4+2\pi\times2^2[/tex]
= [tex]2\pi (24.8 + 4)[/tex]
= [tex] 2\times \frac{22}{7}\times 28.8[/tex]
= [tex] \frac{1267.2}{7}[/tex]
= [tex]181.0 \:cm^2[/tex]
Surface Area of Cylinder = [tex]181.0\: cm^2[/tex]
Part 3.
From given information, cereal box is of cuboid shape.
top & bottom's dimensions are 11 in. × 8 in.
side's dimensions are 11 in. × 6 in.
front & back's dimensions are 8 in. × 6 in.
Dimensions are Length = 11 in. , Width = 8 in. and Height = 6 in.
Surface Area of Cereal Box = Total area of all faces
= Total Surface Area of Cuboid
= 2(Length × Width + Width × Height + Height × Length)
= 2 (11 × 8 + 8 × 6 + 6 × 11)
= 2 (88 + 48 + 66)
= 2 × 202
= 404 [tex]inch^2[/tex]
Surface Area of Cereal Box = 404 [tex]inch^2[/tex]
Part 4.
Given Dimension of Rectangular Prism are Length = 4m , Width = 3m and Heigth = 1m.
Volume of Rectangular Prism = Volume of Cuboid
= length × width × height
= 4 × 3 × 1
= 12 [tex]m^3[/tex]
Volume of Rectangular Prism = 12 [tex]m^3[/tex]
Part 5.
Given, Volume of rectangular Prism is 120 [tex]cm^3[/tex] and length = 5 cm , width = 8 cm
Volume of Rectangular Prism = 120 [tex]cm^3[/tex]
Volume of Cuboid = 120 [tex]cm^3[/tex]
length × width × height = 120
5 × 8 × height = 120
40 × height = 120
height = [tex]\frac{120}{40}[/tex]
height = 30 cm
Height of Prism = 30 cm
Part 6.
The Shape of Newly exposed section is Triangle.
Part 7.
Given dimensions of cylinder are radius, r = 3.5 ft, and height, h = 14 ft
Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]
= [tex]2\pi\times(3.5)\times14+2\pi\times(3.5)^2[/tex]
= [tex]2\pi (49 + 12.25)[/tex]
= [tex] 2\times \frac{22}{7}\times 61.25[/tex]
= [tex] \frac{2695}{7}[/tex]
= [tex]385\: ft^2[/tex]
Volume of Cylinder = [tex]\pi r^2h[/tex]
= [tex]\frac{22}{7}\times(3.5)^2\times14[/tex]
= [tex]\frac{22}{7}\time12.25\times14[/tex]
= [tex]\frac{3773}{7}[/tex]
= [tex]539 \:ft^3[/tex]
Surface Area of Cylinder = [tex]385\: ft^2[/tex]
Volume of Cylinder = [tex]539 \:ft^3[/tex]
