Question

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.Match each approximate volume of a half sphere to the approximate area of the largest cross section of the sphere. Use . 2,789 cubic units 1,796 cubic units 1,287 cubic units 884 cubic units 349 cubic units 575 cubic units 284 square units arrowRight 177 square units arrowRight 380 square units arrowRight 95 square units arrowRight

Answer 1

Answer:

284 square units -----> 1796 cubic units

177 square units -----> 884 cubic units

380 square units -----> 2789 cubic units

95 square units -----> 349 cubic units

Explanation:

The area of the largest cross-section of the sphere is equal to

$A=\pi r^2$

Where r is the radius of the sphere and π = 22/7. Solving for r, we get:

$\begin{gathered} \frac{A}{\pi}=r^2 \\ \\ \sqrt{\frac{A}{\pi}}=r \\ \\ r=\sqrt{\frac{A}{\frac{22}{7}}}=\sqrt{\frac{7A}{22}} \end{gathered}$

Then, with the radius, we will be able to calculate the volume of the half sphere as follows

$\begin{gathered} V=\frac{4}{6}\pi r^3 \\ \\ V=\frac{4}{6}(\frac{22}{7})r^3 \\ \\ V=\frac{44}{21}r^3 \end{gathered}$

Therefore, for each option, we get:

$\begin{gathered} For\text{ A = 284 square units} \\ r=\sqrt{\frac{7(284)}{22}}=9.5 \\ \\ V=\frac{44}{21}(9.05)^3=1796 \\ \\ Answer=1796\text{ cubic units} \end{gathered}$$\begin{gathered} For\text{ A = 177 square units} \\ r=\sqrt{\frac{7(177)}{22}}=7.5 \\ \\ V=\frac{44}{21}(7.5)^3=884 \\ Answer\text{ = 884 cubic units} \end{gathered}$$\begin{gathered} For\text{ A = 380 square units} \\ r=\sqrt{\frac{7(380)}{22}}=11 \\ \\ V=\frac{44}{21}(11)^3=2789 \\ Anwer=2789\text{ cubic units} \end{gathered}$$\begin{gathered} For\text{ A = 95 square units} \\ r=\sqrt{\frac{7(95)}{22}}=5.5 \\ \\ V=\frac{44}{21}(5.5)^3=349 \\ Anwer=349\text{ cubic units} \end{gathered}$

Therefore, the answers are

284 square units -----> 1796 cubic units

177 square units -----> 884 cubic units

380 square units -----> 2789 cubic units

95 square units -----> 349 cubic units