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1 year ago

A cone-shaped pile of gravel has a diameter of 30 m and a height of 9.1 m.

2 answers:

6 0

D/2=r
vcone=(1/3)hpir^2
given
d=30
h=9.1
d/2=30/2=15=r

v=(1/3)9.1pi15^2
v=(9.1/3)pi225
v=682.5pi
use 3.141592 to aprox pi
v=2144.13654
the closese is the first one
answer would be 2120 m³

lapo4ka [179]1 year ago

6 0

Answer: The correct option is (A) 2120 m³.

Step-by-step explanation: Given that a cone-shaped pile of gravel has a diameter of 30 m and a height of 9.1 m.

We are to select the correct option that estimate best approximates the volume of the pile of gravel.

The VOLUME of a cone with radius 'r' units and height 'h' units is given by the formula:

$V=\dfrac{1}{3}\pi r^2h.$

In the given cone-shaped pile, diameter of gravel is 30 m, so its radius will be

$r=\dfrac{30}{2}=15~\textup{m},$

and height, h = 9.1 m.

Therefore, the volume of the cone-shaped pile is

$V\\\\\\=\dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{1}{3}\times 3.14 \times 15^2\times 9.1\\\\\\=3.14\times 75\times 9.1\\\\=2143.05~\textup{m}^3[approx].$

Out of the given options, only 2120 is the nearest one, so the best approximate will be 2120 m³.

Thus, (A) is the correct option.

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Step-by-step explanation:

Given: WXYZ is a parallelogram, ZX ≅ WY

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Proof:

Step 1. WXYZ is a parallelogram and ZX ≅ WY (Given)

Step 2. ZY ≅ WX (Opposite sides of parallelogram are congruent)

Step 3. YX ≅ YX (Reflexive Property)

Step 4. Consider △ZYX and △WXY, we have

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Thus, by SSS rule, △ZYX ≅ △WXY

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Step 6. m∠ZYX ≅ m∠WXY (Definition of congruency)

Step 7. m∠ZYX + m∠WXY = 180° ( consecutive ∠s in a parallelogram are supplementary)

Step 8. m∠ZYX + m∠ZYX = 180° (Substitution)

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