Envision Math Grade 8 Volume 1 Chapter 8 Solve Problems Involving Surface Area And Volume
Page 423 Exercise 1 Answer
Given:
To find the similarity in the figures:
Apply the formula of the cylinder’s volume and the rectangular’s tank volume.
The similarity found in both shapes is the height of the shapes, which is the same.
They are different because both shapes have different volumes.
Given:
From the part(a), the volume of the rectangular tank is greater than the volume of the circular tank.
Since the volume of the rectangular tank is greater than the volume of the circular tank, the rectangular tank can hold more water.
Hence, Ricardo is correct.
Since the volume of the rectangular tank is greater than the volume of the circular tank, the rectangular tank can hold more water. Hence, Ricardo is correct.
Page 424 Essential Question Answer
Volume of cylinder is πr2h, where r = radius and h = height
Prisms and cylinders are similar because they both have two bases and a height.
The formula for the volume of a rectangular solid, V = Bh
V = Bh, can also be used to find the volume of a cylinder when area of base is given.
When area of base is given volume for both cylinder and prism is V = Bh
Page 424 Try It Answer
Given: area = 78.5in2 and height = 11 in
To find: volume of cylinder
We will use the product of area and height to find the volume.
As we know V = Bh then putting all the values
V = 78.5 × 11
= 863.5 in3
Therefore, volume is given as 863.5in3
Page 425 Try It Answer
Given: a cylindrical planter with a base diameter of 15 inches and 5,000 cubic inches is the volume
To find: height of the planter
We will use the formula of volume of cylinder and find the value.
Volume of cylinder is πr2h, where r = radius and h = height
Height of planter is approximately 28 in.
Page 426 Exercise 1 Answer
Volume of cylinder is πr2h, where r = radius and h = height
Prisms and cylinders are similar because they both have two bases and a height.
The formula for the volume of a rectangular solid V = Bh
V = Bh can also be used to find the volume of a cylinder when area of base is given.
When area of base is given volume for both cylinder and prism is V = Bh
Page 426 Exercise 2 Answer
As we know the volume is the product of cross sectional area and height.
Cylinder has a circular base so its area is given as πr2
Now for height h, volume is πr2 × h
Two measurements you need to know to find the volume of a cylinder is radius and height.
Page 426 Exercise 3 Answer
Given: Cylinder A has a greater radius than Cylinder B.
To find: Cylinder A necessarily have a greater volume than Cylinder B?
Volume of cylinder is πr2h, where r = radius and h = height
Volume depends on radius and height both so it is not necessary.
Cylinder A does not necessarily have a greater volume than Cylinder B.
Page 426 Exercise 4 Answer
Given: area is 4πmm2 and height is 10 mm
To find: Volume of Cylinder
We will use the formula and put the values to find volume
As we know that volume is the product of base area and height.
Volume of the cylinder is 40π mm3
Page 426 Exercise 5 Answer
Given: radius is 10 ft and volume is 314 ft3
To find: height of Cylinder
We will use the formula and put the values to find height.
As we know that volume is the product of base area and height.
Volume of cylinder is one feet.
Page 426 Exercise 6 Answer
Given: radius is 4 cm and circumference is 22.4 cm
To find: Volume of Cylinder
First we will find the radius from circumference.
We will use the formula and put the values to find volume.
Volume of the cylinder is 162.8 cm3
Page 427 Exercise 7 Answer
Given: radius is 5 cm and height is 2.5 cm
To find: Volume of Cylinder
We will use the formula and put the values to find volume
As we know that volume is the product of base area and height.
Volume of cylinder is 196.25 cm3
Page 427 Exercise 9 Answer
Given: height is 1 in and volume is 225π in3
To find: radius of Cylinder
We will use the formula and put the values to find radius.
As we know that volume is the product of base area and height.
Radius is calculated as 15 in.
Page 427 Exercise 10 Answer
Given: height is 8.1 cm and volume is 103 cm3
To find: Radius of Cylinder
We will use the formula and put the values to find radius.
As we know that volume is the product of base area and height.
Radius of the bottle is 2.01 cm.
Page 427 Exercise 11 Answer
Given: height is 3 in and radius is 4 in
To find: Volume of Cylinder
We will use the formula and put the values to find volume.
As we know that volume is the product of base area and height.
Putting the values in formula
V = π × 42 × 3
= 48π in3
Volume of the cylinder is 48π in3
Given: height is 3 in and radius is 4 in
To find: is the volume of a cylinder, which has the same radius but twice the height, greater or less than the original cylinder?
We will use the formula and put the values to find radius.
First we will write the original volume and then find the new one.
As we know that volume is the product of base area and height.
The original volume is 48π in3
Now h′ = 2h which will be 6 in
Putting the values in formula
V′ = π × 42 × 6
= 96π in3
Clearly 98π in3 > 48π in3 therefore, volume of second cylinder is greater.
Page 428 Exercise 13 Answer
Given: height is 11.7 in and volume is 885 in3
To find: radius of Cylinder
We will use the formula and put the values to find radius.
As we know that volume is the product of base area and height.
Radius of the cylinder is 4.91 in
Given: height is 11.7 in and volume is 885 cubic inches
To find: If the height of the cylinder is changed, but the volume stays the same, then how will the radius change
We will use the formula of volume and find the dependency of volume.
As we know that volume is the product of base area and height.
That means it is dependent on both radius and height.
V α r2h
If the height of the cylinder is changed, but the volume stays the same, then radius will decrease.
Page 428 Exercise 14 Answer
Given: height is 20.7 cm and diameter is 6.9 cm
To find: Volume of Cylinder
First we will find the radius.
We will use the formula and put the values to find volume.
Volume of the cylinder is 773.6 cm3
Page 428 Exercise 15 Answer
Given: height is 21 in, inner radius is 3 in and outer radius is 5 in
To find: Volume of material
We will use the formula and put the values to find radius.
We will find volume with both the radii and the difference will be required volume
As we know that volume is the product of base area and height.
Putting the values in formula to find outer volume
VR = π × 5 × 5 × 21
VR = 1648.50
As we know that volume is the product of base area and height.
Putting the values in formula for finding volume of inner volume
Vr = π × 3 × 3 × 21
Vr = 593.46
Difference in volumes is
VR − Vr = 1648.50 − 593.46
= 1055.04 in3
Volume of the required material is 1055.04in3
Page 428 Exercise 16 Answer
Given: height is 21 cm and volume is 1029πcm3
To find: radius of Cylinder
We will use the formula and put the values to find radius.
As we know that volume is the product of base area and height.
Radius of the Cylinder is 3.9 cm
Page 428 Exercise 17 Answer
Given: height is 12 yd and diameter is 7 yd
To find: Volume of Cylinder
First we will find the radius.
We will use the formula and put the values to find radius.
Radius is given as \(\frac{\mathrm{d}}{2}=\frac{7}{2}\)
As we know that volume is the product of base area and height.
Volume of cylinder is 147π cubic yards
Page 429 Exercise 1 Answer
A three-dimensional object is in three dimensions having length, width and height.
Example: Cubes, prisms, pyramids, spheres, cones, and cylinders are all examples of three-dimensional objects.
Volume is the product of length, width and height.
Surface areas is the sum of products of length, width and height taken two at a time.
Surface area is a two-dimensional measure.
Volume is a three-dimensional measure.
Page 429 Exercise 3 Answer
Given: A figure of cylinder containing a cone
To find: how much cardboard was used to make the package
First we will find the radius.
Then with the help of tip we will find the surface area.
Radius of the cone is \(\frac{d}{2}\) = 10cm
Putting all the values in the formula
2πrh + 2πr2
S = 2πrh + 2πr2
S = 2π.10.33 + 2π.33.33
= 860π cm2
Surface area for cylinder is 860π cm2
Page 429 Exercise 5 Answer
Given: A figure of sphere with radius as 3 ft
To find: Surface area
Then with the help of tip we will find the surface area.
Putting all the values in the formula of surface area
Surface area of the given sphere is 36π ft2
Page 429 Exercise 6 Answer
Given: Volume is 400πcm3 and diameter is 10 cm
To find: Which option has the correct height
We will use the formula and put the values to find height.
So the height does not match with any of the option (A), (C) or (D).
Correct option is (B).