Question

Round to the nearest whole number if needed and look at the picture for accurate description

Answer 1

The total side area of the figure is 72.8 square inches and the volume is 32 cubic inches.

To solve this, first lets calculate the area of one of the rectangular sides of the object:

Since it's a rectagle of base 2' and height 7', the area is:

`2^(\prime)\cdot7^(\prime)^{}=14in^2`

There are 4 side like this, so we need to multiply it by 4:

`14in^2\cdot4=56in^2`

Next we can calculate the area of the square base. It's a square of side 2', then:

`(2^(\prime))^2=4in^2`

Finally, we need to calculate the area of the piramid on top. Let's find out the area of each triangle.

SInce s = 3.2' is the slant height of the pyramid, that's the height of the triangle, and the base is the same as the whole object: 2'

Then we can use the formula for the area of a triangle:

`A=(h\cdot b)/(2)`

Thus:

`(3.2^(\prime)\cdot2^(\prime))/(2)=3.2in^2`

Before add all, we calculated the area of just one triangle, since there is 4 in the object, we need to multiply by 4:

`3.2in^2\cdot4=12.8in^2`

And now we can add all:

`56in^2+4in^2+12.8in^2=72.8in^2`

Now for the volume, we can calculate first the volume of the pyramid:

`Volume\text{ of a pyramid=}(b^2h)/(3)`

The base of the pyramid is 2' and the height is 3', then:

`((2in)^2\cdot3in)/(3)=4in^3`

For the rectangular prism, we need to multiply the base times the width times the height.

`7^(\prime)\cdot2^(\prime)\cdot2^(\prime)=28in^3`

Added:

`23in^3+4in^3=32in^3`

Then the final answer is 72.8 square inches for the total area and 32 cubic inches for the total volume