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2 years ago

A cone with a height of 4 in, and a diameter of 6 in. Find the surface area and Volume

Mathematics

1 answer:

Vitek1552 [10]2 years ago

8 0

if its diameter is 6, then its radius is half that or 3.

$\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2\qquad \implies \qquad SA=\pi (3)\sqrt{3^2+4^2}+\pi (3)^2 \\\\\\ 3\pi \sqrt{25}+9\pi \implies 3\pi (5)+9\pi \implies 15\pi +9\pi \implies 24\pi$

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" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a

ASHA 777 [7]

Answer:

No, the cone will not hold all of the ice cream.

Step-by-step explanation:

Given:

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let it melt.

Now, to explain mathematically will the cone hold all of the ice cream.

Taking the value of π = 3.14.

So, to get the volume of waffle cone we put formula:

Height (h) = 6 inches.

Diameter = $2\frac{5}{8}=\frac{21}{8}\ inches.$

Thus radius (r) = Diameter ÷ 2 = $\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.$

$Volume=\pi r^2\frac{h}{3}$

$Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}$

$Volume=3.14\times 1.31\times 1.31\times 2$

$Volume=10.78\ inches^3.$

The volume of waffle cone = 10.78 inches³.

Now, to get the volume of scoop which is in the shape of sphere we put formula:

Diameter = $2\frac{7}{8} =\frac{23}{8} \ inches.$

Thus radius (r) = Diameter ÷ 2 $=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.$

$Volume = \frac{4}{3} \pi r^3$

$Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}$

$Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44$

$Volume=12.47\ inches^3.$

The volume of one scoop of ice cream = 12.47 inches³.

So, as the volume of scoop of ice cream is more than the volume of cone.

Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.

Therefore, no the cone will not hold all of the ice cream.

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2 years ago

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Komok [63]

Answer:

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3 years ago

Read 2 more answers

An oxygen tank contained 212 12/3 liters of oxygen before 27 1/3 liters were used. If the tank can hold 240 3/8 liters, how much

lukranit [14]

So, initially 240 $\frac{3}{8}$ -212 $\frac{12}{3}$ were empty:

this is :

$240 \frac{3}{8} - 212 \frac{12}{3} = 240 \frac{3}{8} - 212 +4 = 240 \frac{3}{8} - 216= 24 \frac{3}{8}$

12/4 is 4 so that's why i substituted it with 4.

now, later 27 1/3 were used so we add this tho the original empty space

$24 \frac{3}{8}+ 27 \frac{1}{3}$ = $24 \frac{9}{24}+ 27 \frac{8}{24}$ = $51 \frac{17}{24}$

which is the result!

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3 years ago

How to turn an a equation from standard form into vertex form

alekssr [168]

Is this a real question?

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2 years ago

A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

$t = 3.054$

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

5 0

3 years ago

A cone with a height of 4 in, and a diameter of 6 in. Find the surface area and Volume​

A cone with a height of 4 in, and a diameter of 6 in. Find the surface area and Volume