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GREYUIT [131]
3 years ago
13

For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

the cake is 10 inches. Each edge of the square-shaped base is 8 inches. Find the volume of Mary's cake. Round your answer to the nearest cubic inch.

Mathematics
1 answer:
mihalych1998 [28]3 years ago
4 0

Answer:

V=196in^3

Step-by-step explanation:

The volume of a pyramid is:

V=\frac{A_{b}h}{3}

where A_{b} is the area of the base and h is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

A_{b}=l^2

where l is the length of the side: l=8in, thus:

A_{b}=(8in)^2\\A_{b}=64in^2

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

hypotenuse^2=leg1^2+leg2^2

substituting our values, and indicating that leg 1 is height h:

(10in)^2=h^2+(4in)^2

100in^2=h^2+16in^2

and solving for the height:

h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in

and finally we calculate the volume using this height and the area of the base:

V=\frac{A_{b}h}{3}

V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3

rounding to the nearest cubic inch: V=196in^3

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murzikaleks [220]
So here we're dealing with equivalent fractions.
It's really simple to find the answer, so I'll try to explain the best I can.

2 dogs / 5 cats is really just 2/5.
If we want to find an equivalent fraction, we have to multiply the numerator and the denominator by the same number.

Currently the number of cats is 5, and we need it to be 140. What we need to do is find the number it has to be multiplied by to equal 140, which is 140 divided by 5. 140 divided by 5 is 28, so 5 x 28 = 140!

We need to multiply the denominator (5) by 28, so that we can get 140. What we have now is ?/140.

Like I said, to find an equivalent fraction, we need to multiply the numerator by the same number as we did the denominator, which is 28!

2 x 28 = 56.

So 2/5 is the same as 56/140.

The answer is D) 56 Dogs/140 Cats.

Hope this helps!
If you're confused about anything leave me a reply and I'll try to explain the best that I can!
3 0
3 years ago
Which expression represents the product of s and 39?<br>A=39-s<br>B=39÷s<br>C=39s<br>D=39+s​
Degger [83]
The answer would be c because it means Multiply and whenever a variable is next to a number in this case 39s then that means it a multiplication
So C. 39s
4 0
2 years ago
six times the sum of a number and 3 is 12 less than 12 times the number .Write and solve an equation to fine the number
Aloiza [94]

6 (x+3)=12x-12

6x+18=12x-12

6x-12x=-18-12

-6x=-30

x=5

4 0
3 years ago
The length of a rectangle is twice its width. if the area of the rectangle is 128 ft2 , find its perimeter.
kupik [55]
Length(l)= 2w
Width(w)= w
Area(A) = l*w

A= 128 ft²
128= l*w
128= (2w)w
2w²= 128
w²= 64
w=√64= 8 ft
w= 8 ft

length(l)= 2w
l=2(8)
l=16 ft

P= 2l+2w
P=2(16)+2(8)= 32+16= 48ft
P= 48ft

Answer:
The Perimeter of this rectangle is 48 feet.


Leave any questions you still have in the comments below please! Thank you! Hope this helped! :)
5 0
3 years ago
ONLY THE BRAINLIEST OF USERS ANSWER THIS QUESTION 30 POINTS!!!!!!!!!!!!!!!
denis23 [38]

Answer:

8*5^n-1 / 2^n-1 = n

This is the function for your sequence


3 0
3 years ago
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