Homework 2

Homework 2

If Cuisenaire rods were placed side by side what would happen to the surface area and volume? The first rod is 3 units long, the second is 4 units long, the third is 5 units long. If this pattern were to continue, what would the surface area and volume be when there are 40 rods?

Solution:

According to the given condition, if Cuisenaire rods were placed side by side then we will obtain the following right-angled triangle prism as shown below:

4340

40

Since we need to obtain the surface area and volume of the triangular prism made by

Volume = * base * height

Volume = 0.5 * 43 * 40

Volume = 860

Now the surface area of the obtained figure may be obtained as:

Surface Area = base * height + (perimeter * h)

The perimeter of the obtained figure can only be obtained by the use of hypotenuse, which can be obtained by the use of Pythagoras theorem:

Hyp2 = Perp2 + Base2

Hypotenuse = 58.72

Therefore, surface area will be given as:

Surface Area = 40*43 + (141.72*43)

Surface Area = 7814.31

A sphere with a diameter of 4 cm is cut in half. One of the hemispheres is places on top of a cylinder with a diameter of 4 cm and a height of 3 cm. The cylinder is balanced on the apex of a cone with a radius of 2 cm and a height of 4 cm. What is the surface area that would be exposed to the air or the ground? What is the volume? Write your answer in terms or pi as well as rounded to the nearest tenth.

Solution:

In order to obtain the surface area of the given figure we will proceed as follows:

At first we will obtain the surface area of sphere and divide it by 2 to get the value of the surface area of hemisphere as follows:

Surface area if hemisphere = = = 82

Now, we will obtain the surface area of cylinder as follows:

Surface area of Cylinder = 2 + 2

Since the top face of the cylinder is in contact with the hemisphere, so we proceed as follows:

Surface area of Cylinder = 2 + 2

Surface area of Cylinder = 14

Now, the surface area of the cone will be obtained as:

Surface area of Cone = +

Surface area of Cone = 8

The total surface area of the obtained figure can be obtained as:

Surface Area = 8 + 14 + 8

Surface Area = 30

Now the volume of the given figure may be obtained as follows:

Vol. of Cone =

Vol. of Cone =

Vol. of Cone =

Similarly, Volume of Cylinder may be obtained as:

Vol. of Cylinder =

Vol. of Cylinder =

Vol. of Cylinder =

Volume of hemisphere my also be obtained as:

Vol. of Hemisphere =

Vol. of Hemisphere =

Vol. of Hemisphere =

Finally, the total volume of the obtained figure will be obtained as:

Total Volume = + +

Total Volume =

3. You are walking north along a straight line for 30 paces. You turn and begin walking 20 paces ...