91Ó°ÊÓ

All the edges of a regular triangular pyramid are x units long. Find the volume of the pyramid in terms of x.

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 6\\ w& 3\\ h& \\ \text{L.A.}& \\ \text{T.A.}& \\ V& 54\end{array}$

Suppose the manufacturing company cuts square corners out of pieces of metal that measure 8 inches by 15 inches.

a.Express the volume in terms of x.

b.Find the maximum volume, correct to the nearest tenth of a cubic inch.

c.What are the length, width and height of the box with maximum volume? Give each correct to the nearest tenth of an inch.

Copy and complete the table below for the regular square pyramid.

$\begin{array}{cc}\text{Height},\text{ }h& 24\\ \text{³§±ô²¹²Ô³Ù â¶Ä‰H±ð¾±²µ³ó³Ù},\text{ }l& \\ \text{µþ²¹²õ±ð â¶Ä‰e»å²µ±ð}& 14\\ \text{³¢²¹³Ù±ð°ù²¹±ô â¶Ä‰e»å²µ±ð}& \end{array}$

What kind of figure in each lateral face in the following prism?

V- ABCD is a regular square pyramid. Find the following numerical answers.

$l=\_\_\_$

Find the volume and the total surface area of each solid in terms of the given variables.

The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm³, find the total area of the solid.

A right prism has square bases with edges that are three times as long as the lateral edges. The prism’s total area is 750 m². Find the volume.

A diagonal of a box forms a${35}^{∘}$angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.