# Learning Task 1:Find the volume of the second picture using the volume of the first given. The given solid figures have the same base and height. 1. The volume of the cylinder is 78 cubic cm,find the volume of the cone. 2.The volume of the pyramid is 36 cubic cm,find the volume of the prism. 3.The volume of the cylinder is 198m³, find the volume of the given sphere. 4.The volume of the sphere is 68.5m³,find the volume of the cylinder with the same base and height. The volume of the pyramid is 45.5m³,find the volume of a prism with same base and height . ​pasagot po ng maayos please

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 its 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