The volume of a cube is 36 cm3. What is the surface area of the cube, rounded to the nearest tenth of a cm2
1 answer:
Answer:
65.4 cm²
Step-by-step explanation:
The volume of a cuboid is calculated by multiplying the length, base, and height together. Since a cube has equal sides, the formula for the volume of a cuboid can be simplified as shown below.
Volume of cube
= side ×side ×side
= side³
Given that the volume is 36 cm³, let's find the length of each side.
side³= 36
Cube root both sides:
side=
Total surface area of a cube is the sum of the surface areas of its 6 identical square faces.
Area of a square
= side ×side
= side²
Surface area of 1 face=
Total surface area
=
= 65.416 (5 s.f.)
= 65.4 cm² (nearest tenth)
Additional:
To learn more about surface area of cube, do check out the following!
You might be interested in
Answer:
We conclude that the population proportion is equal to 0.70.
Step-by-step explanation:
We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.
Let p = <u><em>population proportion.</em></u>
(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.
(2) So, Null Hypothesis, : p = 0.70 {means that the population proportion is equal to 0.70}
Alternate Hypothesis, : p < 0.70 {means that the population proportion is less than 0.70}
The test statistics that would be used here <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion = 0.63
n = sample of observations = 100
So, <u><em>the test statistics</em></u> =
= -1.528
The value of z-test statistics is -1.528.
<u>Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.</u>
Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.
Therefore, we conclude that the population proportion is equal to 0.70.
(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.