total outside surface and volume of solids

Question

width13"

length 12

top width 7"

slanted hieght5"

hiegth 4"

Answer 1

Note : If a regular pyramid has a surface area of T square units, a slante height of l units, and its base has a perimeter of P units and an area of B square units, then T = (1 / 2)Pl + B.

Given :

Width (w ) = 13",

Length (l ) = 12",

Height (h ) = 4",

Slanted height (L ) = 5", and

Top width (W ) = 7".

Let us consider that, the pyramid is a rectangular pyramid, then

The perimeter of the base (P )  = 2 ( l + w ).

                                             = 2 ( 12 + 13)

                                             = 2 (15)

                                             = 30".

The area of the base (B ) = l * w

                                        = 12 * 13

                                        = 156 square units.

The total surface area of the solid  T = (1 / 2)PL + B.

Substitute the values of P = 30, L = 5, and B = 156 in T = (1 / 2)PL + B.

T = (1 / 2)(30)(5) + 156

   = 75 + 156

   = 231.

The total outside surface area of the solid is 231 square units.

Note : If a pyramid has a volume of V cubic units, a height of h units, and a base with an area of B square units,

then V = (1 / 3)Bh.

Substitute the values of B = 156 and h = 4 in V = (1 / 3)Bh.

V = (1 / 3)(156)(4)

   = 52 * 4

  = 208 cubic units.

The volume of the solid is 208 cubic units.