Find the surface area of the triangular prism below

QUESTION: To find the surface area of the triangular Prism given in the figure.

STEP BY STEP EXPLANATION:

In a triangular Prism there are three rectangular faces and two triangular faces

As, in the given question the prism is irregular. So, it have different area of base rectangular face than that of the two side rectangular faces.

A/C to the question,

Base of triangular face = 6 unit

Height of triangular face = 4 unit

Length of side rectangular face = 7 unit

Breadth of side rectangular face = 5 unit

Length of base rectangular face = 7 unit

Breadth of base rectangular face = 6 unit

Area of triangle =

Area of rectangle = Length × Breadth

AREA OF PRISM = 2 × AREA OF TRIANGULAR FACE + 2 × AREA OF SIDE RECTANGULAR FACE + AREA OF BASE RECTANGULAR FACE

=> Area of Prism = + 2(Length of side rectangular face × Breadth of side rectangular face) + Length of base rectangular face × Breadth of base rectangular face

=> Area of Prism = + 2(7 × 5) + 7 × 5

=> Area of Prism = 2(3 × 4) + 2(7 × 5) + 7 × 6

=> Area of Prism = 2(12) + 2(35) + 42

=> Area of Prism = 24 + 70 + 42

=> Area of Prism = 136 units²

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hope i

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.