The <u>correct answers</u> are:
1/6πd³;
3; and
9 cm.
Explanation:
For the <u>first question</u>:
The formula for the volume of a sphere is:
We have the diameter, not the radius. The diameter is twice as much as the radius; this means to find the radius using the diameter, we divide by 2. This gives us:
When we raise a fraction to a power, we raise both the numerator and the denominator to that power. This gives us:
We start multiplying this:
For the <u>second question</u>:
The planes of symmetry are the planes through which we can fold the figure in half. These are in the middle horizontally through the figure; in the middle vertically (through the width) through the figure; and in the middle vertically (through the length) through the figure. This makes 3.
For the <u>third question</u>:
The formula for the volume of a triangular prism is:
,
where b is the base of the triangular base of the pyramid, h is the height of the triangular base of the pyramid, and H is the height of the pyramid.
We know the volume is 90; the base of the triangle is 12 and the height is 5:
We divide both sides by 10:
90/10 = 10H/10
9 = H
1/6πd³;
3; and
9 cm.
Explanation:
For the <u>first question</u>:
The formula for the volume of a sphere is:
We have the diameter, not the radius. The diameter is twice as much as the radius; this means to find the radius using the diameter, we divide by 2. This gives us:
When we raise a fraction to a power, we raise both the numerator and the denominator to that power. This gives us:
We start multiplying this:
For the <u>second question</u>:
The planes of symmetry are the planes through which we can fold the figure in half. These are in the middle horizontally through the figure; in the middle vertically (through the width) through the figure; and in the middle vertically (through the length) through the figure. This makes 3.
For the <u>third question</u>:
The formula for the volume of a triangular prism is:
where b is the base of the triangular base of the pyramid, h is the height of the triangular base of the pyramid, and H is the height of the pyramid.
We know the volume is 90; the base of the triangle is 12 and the height is 5:
We divide both sides by 10:
90/10 = 10H/10
9 = H