Answer:
Geometry
Spatial figures are 3-dimensional shapes that can be measured in Cartesian coordinates on the x-axis, y-axis, and z-axis. . With this 3-dimensional shape, it causes the figures to have volume and surface area. Every shape has a formula whether it's volume or surface area.
Further explanation
there are several shapes in the question
1. Cylinder
A cylinder is a geometric figure consisting of 3 sides, namely 2 equal circles and 1 quadrilateral that surrounds the two circles.
volume formula :
\tt V=\pi.r^2.hV=π.r
2
.h
2. Sphere
A sphere is a geometric figure composed of an infinite number of circles.
volume formula :
\tt V=\dfrac{4}{3}\pi r^3V=
3
4
πr
3
3. Cones
A cone is a geometric figure consisting of a circle and a curved plane.
volume formula :
\tt V=\dfrac{1}{3}\pi r^2.hV=
3
1
πr
2
.h
4. Pyramid
A quadrilateral pyramid is a shape that has a rectangular base
volume formula :
\tt V=\dfrac{1}{3}.L.W.hV=
3
1
.L.W.h
Solution
1. V cylinder = 78 cm³
\begin{gathered}\tt V~cylinder=\pi r^2.h=78\\\\V~cone=\dfrac{1}{3}\pi r^2.h=\dfrac{1}{3}\times 78=26~cm^3\end{gathered}
V cylinder=πr
2
.h=78
V cone=
3
1
πr
2
.h=
3
1
×78=26 cm
3
2. V pyramid = 36 cm³
\begin{gathered}\tt V~prism=l.w.h=3\times (\dfrac{1}{3}l.w.h.)=3\times V~pyramid\\\\V~prism=3\times 36=108~cm^3\end{gathered}
V prism=l.w.h=3×(
3
1
l.w.h.)=3×V pyramid
V prism=3×36=108 cm
3
3. V cylinder = 198 cm³
The volume of a sphere is two-thirds the volume of a cylinder.
\begin{gathered}\tt V~cylinder=\pi r^2.h=198\\\\V~sphere=\dfrac{2}{3}\pi r^2.h=\dfrac{2}{3}\times 198=132~cm^3\end{gathered}
V cylinder=πr
2
.h=198
V sphere=
3
2
πr
2
.h=
3
2
×198=132 cm
3
4. V sphere = 67.53 198 cm³
The volume of a sphere is two-thirds the volume of a cylinder.
\begin{gathered}\tt V~sphere=\dfrac{2}{3}.V~cylinder\\\\V~cylinder=\dfrac{3}{2}\times V~sphere\\\\V~cylinder=\dfrac{3}{2}\times 67.53=101.295~cm^3\end{gathered}
V sphere=
3
2
.V cylinder
V cylinder=
2
3
×V sphere
V cylinder=
2
3
×67.53=101.295 cm
3
5. V pyramid = 45.53 cm³
\begin{gathered}\tt V~prism=l.w.h=3\times (\dfrac{1}{3}l.w.h.)=3\times V~pyramid\\\\V~prism=3\times 45.53=136.59~cm^3\end{gathered}
V prism=l.w.h=3×(
3
1
l.w.h.)=3×V pyramid
V prism=3×45.53=136.59 cm
3
