The figure shows a vertical section through the
axis of a solid paper weight made in the shape of a right circular cone. Its height is 8 cm and the diameter of its base is 4 cm. The shaded portion is made of lead 2 cm thick while the unshaded portion is made of wood. The density of lead and wood are 11.3 g/cm and 0.9 g/cm respectively.

Find,
(i) the total volume of the paper weight,
(ii) the volume of the wooden portion,
(iii) the total mass of the paper weight.​

Answer:

i. 33.51 cm³

ii. 14.14 cm³

iii. 231.61 g

Step-by-step explanation:

(i) the total volume of the paper weight,

Since the paper weight is in the form of a cone, its volume is the volume of a cone V = πD²h/12 where D = diameter of cone = 4 cm and h = height of cone = 8 cm

So, V = πD²h/12

V = π(4 cm)² × 8 cm/12

V = 16π cm² × 8 cm/12

V = 128π cm³/12

V = 402.124 cm³/12

V = 33.51 cm³

(ii) the volume of the wooden portion,

The volume of the wooden portion, V' = πr'²h'/3 where r' = radius of wooden portion and h' = height of wooden portion

From similar triangles in the figure, we have

height of wooden portion, h'/radius of wooden portion, r' = height of paper weight, h/radius of paper weight, r

h'/r' = h/r where r = D/2 where D =diameter of paper weight = 4 cm. So, r = 4 cm/2 = 2 cm

and h' = height of paper weight - height of lead portion = 8 cm - 2 cm = 6 cm

So,

r' = rh'/h = 2 cm × 6 cm/8 cm = 12 cm²/8 cm = 1.5 cm

So, V' = πr'²h'/3

V' = π(1.5 cm)² × 6 cm/3

V' = π2.25 cm² × 2 cm

V' = 4.5π cm³

V' = 14.14 cm³

(iii) the total mass of the paper weight.

The total mass of paper weight, m = mass of wooden portion + mass of lead portion = ρ'V' + ρ"V" where ρ' = density of wood = 0.9 g/cm³, V' = volume of wooden portion = , ρ" = density of lead = 11.3 g/cm³ and V" = volume of lead portion = V - V' = 33.51 cm³ - 14.14 cm³ = 19.37 cm³

So, m = 0.9 g/cm³ × 14.14 cm³ + 11.3 g/cm³ × 19.37 cm³

m = 12.726 g + 218.881 g

m = 231.607

m ≅ 231.61 g

How do I find the right answer for b)

I got $2760.38 but the answer is $2760.37

A right triangle has a leg of 12 cm and a hypotenuse of 19 cm.

What is the length of the other leg?

Round to the nearest tenth.
-----------------------------------------
7.0 cm

14.7 cm

22.5 cm

217.0 cm

Find the absolute value of -3.

What is the
average rate of change between:
x = 1 and x = 2?
x = 2 and x = 3?
X = 3 and x = 4?

Which term of series1 +4+7+10+...is43

find the area of the sector (shaded part). Round to the nearest hundredth!

No links!!

Can someone help me please like fast ?

Which of the following represents a coefficient from the expression given?

5x - 21 + x2

anyone know who Howard is ?​

What is the arc measure of major arc ABC in degrees?

What is 72% of 83?

115.3

59.8

190

5100
​

Which three steps are correct when solving this quadratic equation by completing the square?
x2 + 8x + 15 = 0
A)
x4 + 8x = -15
B)
x2 + 8x + 16 - 1
(x + 4)2 = 16
D)
(x + 4)2 = 1
E
x = -3 or x = 5

What is the measure of angle B in degrees?

10$ minus 1.25$ minus 3.18$

A bank loaned out $15,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%?
How much of the $15,000 did the bank loan out at 7%?

Need help fast will give brainiest

add the fractions and simplify the 21/4 + 55/6 + 32/3

A triangular prism has a Volume of 375 cubic units. Find its Volume if all of
its dimensions were reduced to one-fifth their original length?
V=
cubic units.

Can I get some help on this can’t find any of the answers anywhere

Shamus owes his parents $162. He pays them 60% of the $45 he earns as a soccer referee each week. How many weeks will it take Shamus to pay back all of the money he owes his parents?

Use linear regression to find a
function that fits the following
points.
(0,5), (2,-13)

helpppp:((( 10points!!!


14.) Loretta had a pitcher with 165 fl oz of
lemonade to pour into cups at the
birthday party. She filled each cup with
8 fl oz of lemonade until there was not
enough lemonade to completely fill
another cup. How many fluid ounces of
lemonade were left in the pitcher?
F.20 fluid ounces G.5fluid ounces H.21fluid ounces J.157fluid ounces

What is i86?
-i
-1
i
1

The amount of time (in minutes per day) spent on social media for a sample of 10 teens has a mean of 186.7 and a sample standard deviation of 19.99. An independent sample of 8 older adults has a mean of 93.5 minutes with a sample standard deviation of 32.01. Assume that the time spent on social media is approximately normally distributed for each group. a) Determine the value of the test statistic to test H subscript 0 colon space mu subscript t e e n end subscript equals mu subscript o l d e r end subscript against H subscript A colon space mu subscript t e e n end subscript not equal to mu subscript o l d e r end subscript. b) Determine the p-value or critical value for this test at alpha equals 0.05. c) What is your conclusion about whether the two age groups spend the same average amount of time on social media

What percent of 55 is 34?

Need answers ASAP please

plzzz i’ll give brainliest

Please answer ALL and if you do i will give brainliest. URGENT

Given that the measure of ∠x is 149°, and the measure of ∠y is 110°, find the measure of ∠z.

Researchers asked 250 families whether or not they were homeowners and how many cars they had. Their responses are summarized in the following table.
No car or one car Two or more cars
Homeowner
25
90
Not a homeowner
45
90
(a) what percentage of the families are homeowners?
(b) What percentage of the familles have two or more cars?
х
S
?
(b) 1%
Explanation
Check
2021 McGraw-Hill Education. All Rights Reserved. Terms of Use Privacy. Accessibility