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4 years ago

Find the following for the given pyramid: Slant height, lateral area, surface area, and volume. Please show all work!

Mathematics

1 answer:

jolli1 [7]4 years ago

5 0

You have:
1)The slant height is:
Slant height=√[(8 inches)²+(8 inches)²]
Slant height=10 inches
2)The lateral area is:
LA=(Perimeter)(Slant height)/2
LA=(6 inches)(4)(10 inches)/2
LA=120 inches²
3)The Surface area is:
SA=Base area+(PerimeterxSlant height/2)
SA=(6 inches)²+(24 inchesx10 inches/2)
SA=156 inches²
4)The volume is:
V=(6 inches)²(8 inches/3)
V=96 inches³

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The density of ice is approximately 0.92 g/cm3 . If a block of ice has a volume of 2300 cm3, what is its mass?

Mumz [18]

Answer:

The mass of the ice block is 2116 grams ⇒ a

Step-by-step explanation:

The formula of density is $p=\frac{m}{V}$ , where m is the mass and V is the volume

To find the mass from this formula multiply both sides by V,

then m = p.V

∵ The density of ice is approximately 0.92 g/cm³

∴ p = 0.92

- That means the mass of 1 cm³ is 0.92 g

∵ The volume of an ice block is 2300 cm³

∴ V = 2300

- Use the formula of the mass

∵ m = p.V

- Substitute the values of p and V in it

∴ m = (0.92)(2300)

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2 years ago

Find the co-ordinates of the point of trisection of the line joining the points A(1,8) and B(4,2).

Licemer1 [7]

coordinates of the point are (2,6) and (3,4)

Answer:

Solution given:

let the given point be A(1,8) and B(4,2).

P and Q are the two points on AB such that

AP=PQ=QB=k

now

comparing AP and PB

AP=k

PB=2k

ratio of AP and PB = $\frac{1k}{2k}$ = ratio 1:2

now

finding p

for this

$(m_1,m_2)=(1,2)$

For AB

$(x_1,y_1)=(1,8)$

$(x_2,y_2)=(4,2)$

now by using division formula

$(x,y)=(\frac{m_1x_2+m_2x_1}{m_1+m2},\frac{m_1y_2+m_2y_1}{m_1+m2})$

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similarly

Q divides AB

Ratio of AQ and QB = $\frac{2k}{1k}$ = ratio 2:1

$(x_1,y_1)=(1,8)$

$(x_2,y_2)=(4,2)$

$(m_1,m_2)=(2,1)$

by using division formula

$(a,b)=(\frac{m_1x_2+m_2x_1}{m_1+m2},\frac{m_1y_2+m_2y_1}{m_1+m2})$

$=(\frac{2*4+1*1}{2+1},\frac{2*2+1*8}{2+1})=(3,4)$

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