Answer:
3.
Surface Area = 66.4 square centimeters
Volume = 31.52 cubic centimeters
4.
Surface Area = 113.1 square centimeters
Volume = 113.1 cubic centimeters
Step-by-step 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 = [tex]4\pi r^2[/tex]
radius, r, is given as 3, so
Surface Area of Sphere = [tex]4\pi(3)^2=113.1[/tex] square centimeter
Volume of Sphere is given by [tex]\frac{4}{3}\pi r^3[/tex]
We know radius is 3, so
Volume of Sphere = [tex]\frac{4}{3}\pi (3)^3= 113.1[/tex] cubic centimeters
*they are the same
