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3 years ago

Find the height of a cone with a volume of 942 cubic units and a radius of 10 units

1 answer:

3 0

Volume of a cone: $\frac{1}{3}$ $\pi$ r²h
Plug the radius and volume in the formula.

$\frac{1}{3}$ $\pi$ 10²h = 942
Divide both sides by $\frac{1}{3}$ .

$\pi$ 10²h = 2,826
Divide both sides by pi.

10²h = 900
Divide both sides by 10² (100).

h = 9

The cone's height is 9 units.

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What is the total surface area

Stels [109]

We have two right triangles and three different rectangles.

The formula of an area of a right triangle:

$A_T=\dfrac{1}{2}l_1l_2$

l₁, l₂ - legs

We have l₁ = 20cm and l₂ = 21cm. Substitute:

$A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2$

The formula of an area of a rectangle:

$A_R=lw$

l - length

w - width

We have:

rectangle #1: l = 22cm, w = 29cm

$A_{R1}=(22)(29)=638\ cm^2$

rectangle #2: l = 22cm, w = 21cm

$A_{R2}=(22)(21)=462\ cm^2$

rectangle #3: l = 22cm, w = 20cm

$A_{R3}=(22)(20)=440\ cm^2$

The total Surface Area of the triangular prism:

$S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2$

3 0

3 years ago

What expression is equivalent to 24b-34ab

Svet_ta [14]

It should be 2b(12-17a)

8 0

3 years ago

If P is the incenter of JKL, find each measure

d1i1m1o1n [39]

Answer:

Its really simple look it up at some site

6 0

3 years ago

4.) Find the quotient 20 ÷ 1/4 A.) 5 B.) 40 C.) 10 D.) 80

Mazyrski [523]

1/4 of 20 is 5

A is the answer

7 0

3 years ago

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct.

ad-work [718]

Answer:

Probability = 0.190

Step-by-step explanation:

Given:

Number of questions, 'n' = 20

Each question has four choices.

Let event of choosing correct answer be success and its probability be represented by 'p'.

Therefore, event of choosing wrong answer is failure and its probability be represented by 'q'.

Now, probability of success is choosing one correct answer out of 4 options. So, $p=\frac{1}{4}=0.25$

Now, 'p' and 'q' are complements of each other. Therefore,

$q=1-p=1-0.25=0.75$

Now, we need 4 successes. Therefore, $x=4$

Using Bernoulli's theorem to find 'x' successes from 'n' questions, we get:

$P(x)=_{x}^{n}\textrm{C}p^xq^{n-x}$

Plug in 4 for 'x', 20 for 'n', 0.25 for 'p' and 0.75 for 'q'. Solve.

$P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{20-4}\\P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{16}\\P(4)=4845\times (0.25)^4\times (0.65)^{16}\\\\P(4)=0.1896\approx0.190$

Therefore, the probability of getting 4 correct answers out of 20 questions is 0.190.

6 0

3 years ago