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Aloiza [94]
3 years ago
14

Please help me out will mark brainliest :)

Mathematics
1 answer:
Anika [276]3 years ago
4 0

Answer:

AOC

Step-by-step explanation:

Angle COX is formed at vertex O with two rays OC and OX.

Angle AOX is formed at vertex O with two rays OA and OX.

Ray OA lies between rays OC and OX.

All three rays have the common vertex O.

The angle addition postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

So,

m\angle AOX+m\angle AOC=m\angle COX

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A triangle is a three-edged polygon with three vertices. ΔAKE and ΔCKP are congruent.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔABC, since AB≅BC, therefore, the triangle will be an isosceles triangle, and the measure of ∠A ≅ ∠C, using the base angle theorem.

Now In ΔAKE and ΔCKP,

∠A ≅ ∠C {Proved above}

∠AKE ≅ ∠CKP {Given}

AK ≅ KC {Given }

Since two angles and a side of the triangle are equal, therefore, we can write the two triangle are congruent using the Side-angle-side or Angle-Side-Angle congruence.

Hence, ΔAKE and ΔCKP are congruent.

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A sphere is inscribed in a cube with a volume of 64 cubic inches. What is the volume of the sphere? Round your answer to the nea
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Answer:

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Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere and cube.

Given data

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since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,

we know that volume of cube is expressed as

v= l*b*h

v=l^{3}

64= l^{3}

l= \sqrt[3]{64}

l= 4 in

also diameter d=length l

Diameter d=  4in

Radius r =  \frac{d}{2}= \frac{4}{2}= {2 in}

Height h=4in

we know that the volume of a sphere is given by

v= \frac{4}{3} \pi r^{3}

substituting into the formula we have

v= \frac{4}{3} \ *3.142*2^{3} \\v=\frac{4*3.142*8}3} \\v= \frac{100.54}{3} \\v= 33.52in^{3}

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