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Lostsunrise [7]
3 years ago
13

The lengths of the sides of the base of a right square pyramid are 3 feet, and its slant height is 8 feet. If the sides of the b

ase are increased to 9 feet, and the slant height is increased to 24 feet, by what factor is the surface area multiplied? A. 27 B. 9 C. 6 D. 3
Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

Answer:

B. 9

Step-by-step explanation:

The base of a right square pyramid is a square, and we know that the lengths of the square are 3. We can calculate the original area of the base as: 3 * 3 = 9 ft squared.

The slant height is the height of the triangular sides of the pyramid. We know that it's 8 feet, and that the base of the triangle shares a side with the square, so b = 3. Knowing that h = 8 and b = 3, we can apply the triangle area formula: (b * h) / 2 = (8 * 3) / 2 = 24/2 = 12 ft squared. However, there are 4 triangles, so we multiply 12 by 4: 12 * 4 = 48 ft squared.

We add 48 to 9 to get the total original surface area: 48 + 9 = 57 ft squared.

Now, however, the sides of the base of the square are increased to 9 ft, so our new area is 9 * 9 = 81 ft squared.

The slant height becomes 24 ft, so our new triangle area is: (24 * 9)/2 = 216/2 = 108 ft squared. We multiply that by 4: 108 * 4 = 432 ft squared.

The new surface area is thus 81 + 432 = 513 ft squared.

To find the factor the original surface area is multiplied by, we divide 513 by 57: 513 / 57 = 9.

Thus, the answer is B, 9.

Hope this helps!

You might be interested in
1. D=5.9 ft.
Shtirlitz [24]

\qquad\qquad\huge\underline{{\sf Answer}}♨

Here's the solution ~

As we know, we can calculate the circumference of a circle in terms of its diameter as :

\qquad \sf  \dashrightarrow \:c =  \pi d

where, c = circumference and d = diameter

And also, circumference of circle is terms of radius (r) is :

\qquad \sf  \dashrightarrow \:c =  2\pi r

Now, let's move on to questions ~

<h3>First </h3>

\qquad \sf  \dashrightarrow \:3.14 \times 5.9

\qquad \sf  \dashrightarrow \: \approx18.53 \: ft

<h3 />

・ .━━━━━━━†━━━━━━━━━.・

<h3>Second</h3><h3 /><h3 /><h3 /><h3>\qquad \sf  \dashrightarrow \:3.14 \times 3.2</h3>

\qquad \sf  \dashrightarrow \: \approx10.048 \: ft

・ .━━━━━━━†━━━━━━━━━.・

<h3>Third</h3>

\qquad \sf  \dashrightarrow \:3.14 \times 6.1

\qquad \sf  \dashrightarrow \: \approx19.15 \: ft

・ .━━━━━━━†━━━━━━━━━.・

<h3>Fourth</h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  3.7

\qquad \sf  \dashrightarrow \: \approx2×11.62  \: m

\qquad \sf  \dashrightarrow \: \approx23.24  \: m

・ .━━━━━━━†━━━━━━━━━.・

<h3>Fifth </h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  6.2

\qquad \sf  \dashrightarrow \: \approx2× 19.47 \: units

\qquad \sf  \dashrightarrow \: \approx38.94  \: m

・ .━━━━━━━†━━━━━━━━━.・

<h3>Sixth</h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  5.1

\qquad \sf  \dashrightarrow \: \approx2×16.01 \: ft

\qquad \sf  \dashrightarrow \: \approx \: 32.02m

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

7 0
2 years ago
Algebra help please I need a equation please
Rudik [331]
K = s + 4
k + s = 26
s + 4 = 26
Subtract 4 from both sides of the equation.
s = 22
Steve ran 22 miles.
3 0
3 years ago
Please help me. I really appreciate it if you answered. Thank you! &lt;3
exis [7]

Answer:

$3100 is invested at 9%

$4900 is invested at 11%

Step-by-step explanation:

Let's take "x" be the amount invested at 9%.

(x + 1800) is invested in another account at 11%.

The interest amount earned by the two accounts is $818.

Here we can use the simple interest formula and find the amount invested in each account.

Simple interest (I) = , where P- is the principal , N is the number of years and R is the interest rate.

Simple interest =

0.09x + 0.11(x+1800) = 818

Now we have to simplify and find the value of x .

Use the distributive property and simplify the second term.

0.09x + 0.11x + 198 = 818

0.2x + 198 = 818  

0.2x =818 - 198

0.2x = 620

x = 620/0.2

x = 3100.

So $3100 is invested at 9%

x + 1800 = 3100 + 1800

= $4900

$4900 is invested at 11%

Hope this helped.

6 0
3 years ago
A bonus of £2100 is shared by 10 people who work for a company. 40 percent of the bonus is shared equally between 3 managers. Th
Alja [10]

Answer:

Salesman is not correct

Step-by-step explanation:

First we calculate the share of salesman when 60 percent of bonus is shared among 7 salesmen:

Bonus Share For 7 Salesmen = (0.6)(£ 2100)

Bonus Share For 7 Salesmen = £ 1260

Now, this is equally divided among 7 salesmen:

Bonus Share of 1 Salesmen (when 60% is shared) = S₁ = £ 1260/7

S₁ = £ 180

Now, we calculate the share each salesmen get if bonus is equally divided among 10 people:

Bonus Share of 1 Salesmen (when equally shared) = S₂ = £ 2100/10

S₂ = £ 210

S₂/S₁ = £ 210/£ 180

S₂/S₁ = 1.16

S₂ = 1.16S₁

S₂ = 116% of S₁

This means that if bonus is equally divided between all 10 people then the salesman will get 16 percent more money.

<u>Therefore, salesman is not correct</u>

6 0
3 years ago
Tìm giá trị của x đẻ căn thức sau có ý nghĩa<br> √(3x-6)
jolli1 [7]

Answer:

đoán xem

Step-by-step explanation:

4 0
3 years ago
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