Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Two square based pyramids are joined, total volume is 2700mm, perpendicular height of top pyramid is 16mm, perpendicular height of bottom pyramid is 20mm, length and width of joint base area both x, find x. Please help me

Sagot :

Answer: 15 m

Step-by-step explanation:

Given

Total volume of the combined pyramid is [tex]V=2700\ mm^3[/tex]

Height of top and bottom pyramid is

[tex]h_t=16\ mm[/tex]

[tex]h_b=20\ mm[/tex]

If the base has a side length of x, its area must be [tex]x^2[/tex]

Volume of square prism is given by

[tex]\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm[/tex]

Thus, the value of [tex]x[/tex] is 15 m.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.