Question

1. Find the surface area of the prism. L=12m/W=5m/H=9m

2. Find the surface are of the cylinder to the nearest tenth. L=4cm/H=12.4cm


3. When Tyson opens and lays a cereal box out flat, he sees that the top and the bottom of the box both measure 11 inches by 8 inches, the sides of the box both measure 11 inches by 6 inches, and the front of the box and back of the box both measure 8 inches by 6 inches. What is the surface area of Tyson's cereal box


4. Find the volume of the rectangular prism. L=4m/W=3m/H=1m


5. A rectangular prism has a volume of 120cm3. Its length is 5cm and its width is 8cm. What is the prism's height


6. Starting at the top, if you cut a square pyramid in half using a single cut, what is the shape of the newly-exposed section


7. The radius of a cylinder is 3.5ft. The height is 14ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. Show your work.

Answer 1

1. Surface Area of Prism = 426
`\,m^2`

2. Surface Area of Cylinder =
`181.0 \:cm^2`

3. Surface Area of Cereal Box = 404
`\,inch^2`

4. Volume of Rectangular Prism = 12
`m^3`

5. Height of Prism = 30 cm

6. The Shape of Newly exposed section is Triangle.

7. Surface Area of Cylinder =
`385 \:ft^2`

Volume of Cylinder =
`539 \:ft^3`

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
`\,m^2`

Surface Area of Prism = 426
`\,m^2`

Part 2.

Given Dimension of cylinder are length or diameter = 4 cm and Height, h = 12.4 cm

radius, r =
`(Diameter)/(2)`

=
`(4)/(2)` = 2 cm

Surface Area of Cylinder =
`2\pi rh+2\pi r^2`

=
`2\pi *2*12.4+2\pi*2^2`

=
`2\pi (24.8 + 4)`

=
`2* (22)/(7)* 28.8`

=
`(1267.2)/(7)`

=
`181.0 \:cm^2`

Surface Area of Cylinder =
`181.0\: cm^2`

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
`inch^2`

Surface Area of Cereal Box = 404
`inch^2`

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
`m^3`

Volume of Rectangular Prism = 12
`m^3`

Part 5.

Given, Volume of rectangular Prism is 120
`cm^3` and length = 5 cm , width = 8 cm

Volume of Rectangular Prism = 120
`cm^3`

Volume of Cuboid = 120
`cm^3`

length × width × height = 120

5 × 8 × height = 120

40 × height = 120

height =
`(120)/(40)`

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 =
`2\pi rh+2\pi r^2`

=
`2\pi*(3.5)*14+2\pi*(3.5)^2`

=
`2\pi (49 + 12.25)`

=
`2* (22)/(7)* 61.25`

=
`(2695)/(7)`

=
`385\: ft^2`

Volume of Cylinder =
`\pi r^2h`

=
`(22)/(7)*(3.5)^2*14`

=
`(22)/(7)\time12.25*14`

=
`(3773)/(7)`

=
`539 \:ft^3`

Surface Area of Cylinder =
`385\: ft^2`

Volume of Cylinder =
`539 \:ft^3`

Answer 2

Part 1) The surface area of the prism is equal to
`202\ m^(2)`

Part 2) The surface area of the cylinder is equal to
`412.0\ cm^(2)`

Part 3) The surface area of Tyson's cereal box is
`404\ in^(2)`

part 4) The volume of rectangular prism is
`12\ m^(3)`

Part 5) The prism's height is
`3\ cm`

Part 6) The shape of the newly-exposed section is a triangle

Part 7)

Part a) The surface area of cylinder is
`384.7\ ft^(2)`

Part b) The volume of cylinder is
`538.5\ ft^(3)`

Explanation:

Part 1)

The surface area of the prism is equal to

`SA=2B+Ph`

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

`B=LW=4*5=20\ m^(2)`

Find the perimeter of the base P

`P=2(L+W)=2(4+5)=18\ m`

`h=9\ m`

Find the surface area

`SA=2B+Ph` ---->
`SA=2(20)+18(9)=202\ m^(2)`

Part 2)

The surface area of the cylinder is equal to

`SA=2\pi r^(2) +2\pi r(h)`

we have

`r=4\ cm`

`h=12.4\ cm`

Find the surface area

assume
`\pi =3.14`

`SA=2\pi (4^(2)) +2\pi (4)(12.4)=131.2\pi=412.0\ cm^(2)`

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

`A=2(11*8)=176\ in^(2)`

Area of the sides

`A=2(11*6)=132\ in^(2)`

Area of the front and the back

`A=2(8*6)=96\ in^(2)`

The surface area is equal to

`SA=176+132+96=404\ in^(2)`

Part 4) we know that

The volume of rectangular prism is equal to

`V=LWH`

substitute the values

`V=4*3*1=12\ m^(3)`

Part 5) we know that

The volume of rectangular prism is equal to

`V=LWH`

solve for H

`H=V/(LW)`

substitute the values

`H=120/(5*8)=3\ cm`

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

`SA=2\pi r^(2) +2\pi r(h)`

we have

`r=3.5\ ft`

`h=14\ ft`

Find the surface area

assume
`\pi =3.14`

substitute

`SA=2\pi (3.5^(2)) +2\pi (3.5*14)=122.5\pi=384.7\ ft^(2)`

Part b) we know that

The volume of a cylinder is equal to

`V=\pi r^(2)h`

we have

`r=3.5\ ft`

`h=14\ ft`

assume
`\pi =3.14`

substitute the values

`V=\pi (3.5^(2))(14)=171.5\pi=538.5\ ft^(3)`