Question

Hey there! I was wondering if I could receive help on solving these first 4 questions! At least an explanation on how I could solve them myself would be fine :)

Answer 1

1.

This figure is a rectangular prism. The surface area of a rectangular prism is given by:

$\begin{gathered} SA=2(lw+lh+wh) \\ Where: \\ l=14cm \\ w=11cm \\ h=14cm \end{gathered}$

So:

$\begin{gathered} SA=2(14\cdot11+14\cdot14+11\cdot14) \\ SA=2(154+196+154) \\ SA=2(504) \\ SA=1008cm^2 \end{gathered}$

The volume of the rectangular prism is:

$\begin{gathered} V=l\cdot w\cdot h \\ V=14\cdot11\cdot14 \\ V=2156cm^3 \end{gathered}$

2.

The surface area of the sphere is:

$SA=4\pi r^2$

And the volume is:

$V=\frac{4}{3}\pi r^3$

Where:

$\begin{gathered} r=\frac{20}{2} \\ r=10 \end{gathered}$

3.

The surface area of the cylinder is:

$SA=2\pi r^2+2\pi rh$

And the volume is:

$\begin{gathered} V=\pi r^2h \\ \end{gathered}$

Where:

$\begin{gathered} r=\frac{19}{2} \\ r=9.5 \\ h=19 \end{gathered}$

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4.

The surface area of the triangular prism is:

$SA=ls+bh+lb+lr$

And the volume is:

$V=\frac{1}{2}lbh$

Where:

$\begin{gathered} l=15 \\ s=22 \\ r=19 \\ h=18 \\ b=16 \end{gathered}$