Answered

At IDNLearn.com, find answers to your most pressing questions from experts and enthusiasts alike. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

Helpppp!!!

Determine the volume of Sirius' doghouse to the nearest hundredth of a cubic metre.

Helpppp Determine The Volume Of Sirius Doghouse To The Nearest Hundredth Of A Cubic Metre class=

Sagot :

Sqdancefanidn

Answer:

  1.28 cubic meters

Step-by-step explanation:

You want the volume of the pentagonal prism shown.

End area

The area of a pentagonal face of the doghouse is that of a triangle together with a rectangle. It will be the same as that of a trapezoid of the same width with one base equal to the full height, and the other base equal to the rectangle height.

  A = triangle + rectangle

  A = (1/2)(1.2 -0.7)(0.9) +(0.7)(0.9)

  A = (1/2)(1.2 +0.7)(0.9)

Volume

The volume is the product of the end area and the length of the doghouse.

  V = Bh . . . . . . where B is the area of the base, and h is the "height" (length) of the prism

  V = (1/2)(1.2 +0.7)(0.9)(1.5) = 1.2825 . . . . cubic meters

The volume of the doghouse is about 1.28 cubic meters.

__

Additional comment

As you know from the formula for the area of a triangle, its area is equivalent to that of a rectangle with the same base and half the height. That makes it convenient to redraw the figure as being a cuboid with height equal to the average of the 70 cm dimension and the 1.2 m dimension.

View image Sqdancefan
Olumideolawoyinidn

Answer:

1.28m³

Step-by-step explanation:

Sirius' doghouse structure into two parts:

Upper structure and the base structure.

Volume of the upper structure = volume of a prism with isosceles base triangle.

Volume of the upper structure = base area × height of the prism

= 2 × 1/2bh × height of the prism

= bh × height of the prism

= 0.45m × 0.5m × 1.5m

= 0.3375m³

Volume of the base structure =

volume of a rectangular prism

= length × width × height

= 1.5 × 0.9 × 0.7

= 0.945m³

Therefore, the volume of Sirius' doghouse

= Volume of the upper structure + Volume of the base structure

= 0.3375m³ + 0.945m³

= 1.2825 m³

= 1.28m³ to the nearest hundredth.

View image Olumideolawoyin
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.