Question

See the picture below

Answer 1

3.

Surface Area = 66.4 square centimeters

Volume = 31.52 cubic centimeters

4.

Surface Area = 113.1 square centimeters

Volume = 113.1 cubic centimeters

Explanation:

3.

Surface area of pyramid is area of all the surfaces. There are 4 triangles with area 1/2 * base * height

Where base is 4 and height is 6.3

Area of 4 triangles = 4 * 1/2 * 4 * 6.3 = 50.4

And area of square which is base^2 = 4 ^ 2 = 16

Surface Area = 50.4 + 16 = 66.4 square centimeters

Volume of Pyramid is 1/3 * area of base * height

To find height, altitude, we can drop from vertex to middle bottom. Now we can create a right triangle with hypotenuse 6.3 and base 2 (half of the side 4 cm). The altitute (height) is the other leg.

Now we can use pythagorean theorem to find height:

height ^ 2 + 2 ^ 2 = 6.3 ^ 2

height^2 + 4 = 39.69

height^2 = 39.69 - 4

height^2 = 35.69

height = 5.97

Now, Volume of Pyramid = 1/3 * (4)^2 * 5.97 = 31.52 cubic centimeters

4.

Surface area of sphere is given by:

Surface Area of Sphere =
`4\pi r^2`

radius, r, is given as 3, so

Surface Area of Sphere =
`4\pi(3)^2=113.1` square centimeter

Volume of Sphere is given by
`(4)/(3)\pi r^3`

We know radius is 3, so

Volume of Sphere =
`(4)/(3)\pi (3)^3= 113.1` cubic centimeters

*they are the same