All categories

3 years ago

What is the volume of the square-based pyramid?

Mathematics

1 answer:

grandymaker [24]3 years ago

6 0

Answer:

Volume of square-based pyramid = 96 in³

Step-by-step explanation:

Given:

Base side of square = 6 inch

Height of pyramid = 8 inch

Find:

Volume of square-based pyramid

Computation:

Area of square base = Side x Side

Area of square base = 6 x 6

Area of square base = 36 in²

Volume of square-based pyramid = (1/3)(A)(h)

Volume of square-based pyramid = (1/3)(36)(8)

Volume of square-based pyramid = (12)(8)

Volume of square-based pyramid = 96 in³

You might be interested in

Sam traveled 3/4 of a journey by bus. He jogged 1/2 of the remaining distance and walked the rest of the way. If he walked 800 f

Troyanec [42]

Let x = total distance he covered
3x/4 by bus
1/2 . x/4 = x/8 by jogging
the remaining distance = x/8 by walking
thus x/8 = 800ft
x = 8 . 800 = 6400ft

3 0

3 years ago

Fill in the blank to this mathematics question

lorasvet [3.4K]

Answer:

x = 24 makes the original equation true

Step-by-step explanation:

2 < x ≤ 24

2 < x signifies x cannot be equal to 2

x≤24 signifies x can be equal to 24.

3 0

3 years ago

When written in scientific notation, the number 4,500 will have a Choose... 2 4 3 as the exponent on the power of ten

nexus9112 [7]

The exponent would be 3.
4.5 x 10^3

6 0

3 years ago

Which is a correct definition of perpendicular lines?

djyliett [7]

It would be B: a set of points that extends infinitely in two directions

4 0

2 years ago

G verify that the divergence theorem is true for the vector field f on the region

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv$

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

3 0

3 years ago