Answer:
1.-urface AreaRectangular Prism:Surface Area = 2lw + 2lh + 2whwhere l is length, w is width, and h is height.Cylinder:Surface Area = 2πrh + 2πr2where r is the radius and h is the height.Sphere:Surface Area = 4πr2where r is the radius.Cone:Surface Area = πr(r + sqrt(h2 + r2))where r is the radius and h is the height.VolumeRectangular Prism:Volume = lwhwhere l is length, w is width, and h is height.Cylinder:Volume = πr2hwhere r is the radius and h is the height.Sphere:Volume = (4/3)πr3where r is the radius.Cone:Volume = (1/3)πr2hwhere r is the radius and h is the height.Diving Deeper into FormulasRectangular Prism
The surface area of a rectangular prism is calculated by adding the areas of all six faces. Each pair of faces (top/bottom, front/back, left/right) has the same area, and thus, the formula is derived by summing up these pairs. The volume is simply the product of the length, width, and height, representing the cubic space enclosed by the prism.
Cylinder
2.-The surface area of a cylinder is found by calculating the areas of the two circular bases and the rectangular wrap around its side. The volume is derived by multiplying the area of the base circle with the height, representing the cubic space it encloses.
Sphere
3.-A sphere's surface area is calculated using the square of the radius, multiplied by 4π, representing the total area covered by the curved surface. The volume is found by cubing the radius, multiplying by π, and then multiplying by (4/3), indicating the cubic space within the sphere.
Cone
4.-The surface area of a cone is found by adding the area of the base circle and the lateral area, which is shaped like a sector of a circle. The volume is calculated by taking the area of the base, multiplying it by the height, and then dividing by 3, representing the cubic space within the cone.