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2 years ago

A pyramid has a square base that measures 20 inches on each side and 30 inches high. Find the volume of the pyramid.

Mathematics

1 answer:

irinina [24]2 years ago

7 0

The volume of pyramid is 4000 inch³.

<h3>What is Volume?</h3>

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc. Volume is sometimes referred to as capacity.

The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Given:

base = 20 inches

height = 30 inches

Now, volume of pyramid

Volume = a²h/3

Volume = 20 x 20 x 30 /3

Volume = 400 x 10

Volume = 4000 inch³

Hence, the volume of pyramid is 4000 inch³.

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3 years ago

Find the 8th term of the geometric sequence whose common ratio is 2/3 and whose first term is 7

motikmotik

Answer:

The 8th term of the sequence is 896/2187.

Step-by-step explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

$\displaystyle x_{n} = a\left(r\right)^{n-1}$

Where <em>a</em> is the initial term and <em>r</em> is the common ratio.

Substitute:

$\displaystyle x_{n} = 7\left(\frac{2}{3}\right)^{n-1}$

To find the 8th term, let <em>n</em> = 8. Substitute and evaluate:

$\displaystyle \begin{aligned} x_{8} &= 7\left(\frac{2}{3}\right)^{(8) - 1} \\ \\ &= 7\left(\frac{2}{3}\right)^{7} \\ \\ &= 7\left(\frac{128}{2187}\right) \\ \\ &= \frac{896}{2187} = 0.4096...\end{aligned}$

In conclusion, the 8th term of the sequence is 896/2187.

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