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3 years ago

Given a cube with a volume of 36 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

2 answers:

5 0

Hope you know that formula for volume of a cube is area of base time height
and volume of a square pyramid is area of base time height divide 3
- so in this your exercise case we know that area of cube is 36 cm^3 what is area of base time height
- so this mean that the volume of a square pyramide what can fit perfectly inside the cube will be equal 36/3 = 12 cm^3

stiv31 [10]3 years ago

3 0

Answer:

$\text{The volume of square pyramid is}12cm^3$

Step-by-step explanation:

Given a cube with a volume of 36 cubic centimeter. we have to find the volume of square pyramid that can fit perfectly inside the cube.

As the pyramid base is same as the side of cube

$\text{Volume of cube is }a^3$

$\text{Volume of square pyramid is=}\frac{a^3}{3}$ (∵a=h)

i.e the volume of square pyramid is one-third of the volume of cube.

∴ $\text{Volume of square pyramid is=}\frac{1}{3}\times\text{Volume of square pyramid}$

$=\frac{36}{3}=12cm^3$

Hence, $\text{the volume of square pyramid is}12cm^3$

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<h3>Answer: </h3><h3>Overall balance for year 5 after taxes = $1350</h3><h3>The filled out table is shown in the attached image below</h3>

===============================================================

Work Shown:

10% = 10/100 = 0.10

10% of 1000 = 0.10*1000 = 100 is the amount of interest earned in year 1. This goes in the first row of column 1. The overall balance becomes 1000+100 = 1100 after we add on the interest earned. We will write 1100 in row1,column2.

Next, compute the tax: 30% of 100 = 0.30*100 = 30. The 30 will be written in row1,column3. Finally, we subtract the amount taxed (30) from the overall balance in column 2 (which was 1100). So 1100-30 = 1070 will be written in row1,column4.

After finishing row1, we should have these four values: 100, 1100, 30, 1070

----------------------------------------------

Now onto row 2

We earn the same amount in interest because we are not compounding. Write 100 in row2,column1.

The overall balance will be different. Instead of using 1000, we will use 1070 which was the figure in row1,column4. Add the amount of interest earned ($100) onto the updated balance ($1070) to get 1170. Write 1170 in row2,column2

The value in row2,column3 is the same as the value above it. This is because the amount of interest does not change, so the amount taxed doesn't change either. Basically we'll have 30s all the way down column 3. We'll also have 100s all the way down column 1.

Subtract 1170 and 30 to get 1140 which is the balance after taxes for year 2.

------------------------------------------------

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2 years ago

{HIGH PAYOUT} Can someone help by showing work on how to get to answer?

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Let's assume each line is one toothpick.

In figure 1, there is a square made out of the 4 toothpicks.

In figure 2, there are four squares made. However, the 4 four toothpicks were already used, so we don't count them twice. That gives 4 (that were used) + 3 (the new ones on the left) + 3 (new ones on top) + 3 (new ones on right). We sum them up: 4 + 3 + 3 + 3 = 13.

In figure 3 there are nine squares made. We have the 13 squares made, plus 3 on the left column, 2 on the left center column, 3, on the center column, 2 on the right center, and 3 on the right. We total them up. 13 + 3 + 2 + 3 + 2+ 3 = 26.

Let's look at the pattern.

<u>Figure #</u> <u># Toothpick</u>s

1 4

2 13

3 26

From figure 1 to 2, we added 9. From 2 to 3 we added 13. If we draw figure 4, we would add (from left to right) 3, 2, 2, 3, 2, 2, 3. That would be 17 toothpicks added, and 39 total. Let's go back to the table.

<u>Figure #</u> <u># Toothpick</u>

1 4

2 13

3 26

4 39

Now let's look at the sequence happening. As we add more, we increase by 9, then 13, then 17. For each row, we add the same number as the previous row and then add 4. Drawing Figure 5 would be too much, but we can conclude based on the pattern that 21 squares would be added. We can take this sequence as far as we need to. We want the 10th figure or term, so we apply the pattern and keep going until we get there.

<u>Figure #</u> <u># Toothpick</u>

1 4

2 13 <--- add 9

3 26 <--- add 13, the same 9 and 4 more

4 39 <--- add 17, the same 13 and 4 more

5 60 <--- add 21, the same 17 and 4 more

6 85 <-- add 25, the same 21 and 4 more

7 114 <-- add 29, the same 25 and 4 more

8 147 <-- add 33

9 184 <---- add 37

10 225 <-- add 41

Thus the 10th figure has 225 toothpicks.

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alina1380 [7]

In ∆ABD

$\\ \sf\longmapsto Area=\dfrac{1}{2}bh=\dfrac{1}{2}(7\times 4)$

In ∆BCD

$\\ \sf\longmapsto Area=\dfrac{1}{2}(7\times 4)$

Now

IN PARALLELOGRAM ABCD

$\\ \sf\longmapsto Area=\dfrac{1}{2}(7\times 4)+\dfrac{1}{2}(7\times 4)$

Option A

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