Surface area: Substitute the values of the radius <span>(<span><span>r=5</span>),</span></span><span> the </span>height <span>(<span><span>h=9</span>),</span></span><span> and an approximation for </span><span>π(3.14)</span><span> into the </span>formula<span>. </span><span>SA=2(3.14)(5<span>)^2</span>+2(3.14)(5)(9)
</span>Simplify each term<span>. </span><span>SA=157+282.6 </span> Add 157<span> and </span>282.6<span> to get </span><span>439.6. </span><span>Surface area=439.6cm^2
Volume: </span>Substitute the values of the radius <span>(<span><span>r=5</span>),</span></span><span> the </span>height <span>(<span><span>h=9</span>),</span></span><span> and an approximation of </span>Pi <span>(<span>3.14)</span></span><span> into the </span>formula<span> to find the </span>volume<span> of the </span>cylinder<span>. </span><span>V≈3.14⋅<span>5^2</span>⋅9
</span>Raise 5<span> to the </span>power<span> of </span>2<span> to get </span><span>25. </span><span>V≈+3.14⋅25⋅9
Surface area: Substitute the values of the radius <span>(<span><span>r=9</span>),</span></span><span> the </span>height <span>(<span><span>h=24</span>),</span></span><span> and an approximation for </span><span>π(3.14)</span><span> into the </span>formula<span>. </span><span>SA=2(3.14)(9<span>)^2</span>+2(3.14)(9)(24)
</span>Simplify each term<span>. </span><span>SA=508.68+1356.48
</span>Add 508.68<span> and </span>1356.48<span> to get </span><span>1865.16. Surface area = </span>1865.16<span>i<span>n^2
Volume: </span></span>Substitute the values of the radius <span>(<span><span>r=9</span>),</span></span><span> the </span>height <span>(<span><span>h=24</span>),</span></span><span> and an approximation of </span>Pi <span>(<span>3.14)</span></span><span> into the </span>formula<span> to find the </span>volume<span> of the </span>cylinder<span>. </span><span>V≈3.14⋅<span>9^2</span>⋅24
</span>Raise 9<span> to the </span>power<span> of </span>2<span> to get </span><span>81. </span><span>V≈+3.14⋅81⋅24 </span>Multiply 3.14<span> by </span>81<span> to get </span><span>254.34. </span><span>V≈+254.34⋅24 </span>Multiply 254.34<span> by </span>24<span> to get </span><span>6104.16.
Surface area: Substitute the values of the radius <span>(<span><span>r=10</span>),</span></span><span> the </span>height <span>(<span><span>h=15.5</span>),</span></span><span> and an approximation for </span><span>π(3.14)</span><span> into the </span>formula<span>. </span><span>SA=2(3.14)(10<span>)^2</span>+2(3.14)(10)(15.5) </span> Simplify each term<span>. </span><span>SA=628+973.4 </span>Add 628<span> and </span>973.4<span> to get </span><span>1601.4. </span><span>SA=1601.4 Surface area=</span>1601.4<span>c<span>m^2
Volume: </span></span>Substitute the values of the radius <span>(<span><span>r=10</span>),</span></span><span> the </span>height <span>(<span><span>h=15.5</span>),</span></span><span> and an approximation of </span>Pi <span>(<span>3.14)</span></span><span> into the </span>formula<span> to find the </span>volume<span> of the </span>cylinder<span>. </span><span>V≈3.14⋅<span>10^2</span>⋅15.5
</span>Group coefficients<span> together and </span>exponents<span> together to </span>multiply<span> numbers in </span>scientific notation<span>. </span><span>V≈+(3.14⋅15.5)(<span>10^2</span>) </span>Multiply 3.14<span> by </span>15.5<span> to get </span><span>48.67. </span><span>V≈+48.67⋅<span>10^2 </span></span>Write <span>48.67⋅<span>10^2</span></span><span> in proper </span>scientific notation<span>. </span> <span>V≈+4.867⋅<span>10^3</span></span><span>c<span>m^3
Surface area: Substitute the values of the radius <span>(<span><span>r=24</span>),</span></span><span> the </span>height <span>(<span><span>h=6</span>),</span></span><span> and an approximation for </span><span>π(3.14)</span><span> into the </span>formula<span>. </span><span>SA=2(3.14)(24<span>)^2</span>+2(3.14)(24)(6)
</span>Simplify each term<span>. </span><span>SA=3617.28+904.32 </span>Add 3617.28<span> and </span>904.32<span> to get </span><span>4521.6. </span><span>SA=4521.6 Surface area=</span>4521.6<span>i<span>n^2
Volume: </span></span>Substitute the values of the radius <span>(<span><span>r=24</span>),</span></span><span> the </span>height <span>(<span><span>h=6</span>),</span></span><span> and an approximation of </span>Pi <span>(<span>3.14)</span></span><span> into the </span>formula<span> to find the </span>volume<span> of the </span>cylinder<span>. </span><span>V≈3.14⋅<span>24^2</span>⋅6
</span>Raise 24<span> to the </span>power<span> of </span>2<span> to get </span><span>576. </span><span>V≈+3.14⋅576⋅6 </span>Multiply 3.14<span> by </span>576<span> to get </span><span>1808.64. </span><span>V≈+1808.64⋅6 </span>Multiply 1808.64<span> by </span>6<span> to get </span><span>10851.84. </span> <span>V≈+10851.84</span><span>i<span>n^3
To solve the second part to the problem just find the two items in your home and solve for the circumference, surface area, and volume. You can look back at my steps for formulas if you need help.</span></span>
We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.
