1. The volume of the cylinder is 78 cubic cm, find the volume of the cone.
​

The volume of a cylinder = 78 \mathrm{cm}^{3}78cm3

Let us substitute the volume of cylinder in the formula.

The formula for volume of a cone is V=\frac{\pi r^{2} h}{3}V=3πr2h                    (1)

The formula for volume of a cylinder is V=\pi r^{2} hV=πr2h              (2)

Substituting V=78V=78 in equation (2), we get,

\begin{gathered}\begin{array}{c}{V=\pi r^{2} h} \\{78=\pi r^{2} h}\end{array}\end{gathered}V=πr2h78=πr2h

Given that the cone has the same radius and height of that of the cylinder, let us substitute 78=\pi r^{2} h78=πr2h in equation (1)

\begin{gathered}\begin{array}{l}{V=\frac{\pi r^{2} h}{3}} \\{V=\frac{78}{3}} \\{V=26}\end{array}\end{gathered}V=3πr2hV=378V=26

Thus, the volume of a cone with the same radius and height of a cylinder is 26 \mathrm{cm}^{3}26cm3 .

26 cm^3 I hope this helps!

Step-by-step explanation:

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it