Question

Math questions! Please help?

Answer 1

Hello there.

What is the volume of the given prism?

9.4 * 5.4 * 11.7=593.892

Round to the nearest tenth of a centimeter 

Based off that, 

Answer: 593.9. 
Second Option.

Answer 2

Answer:

Step-by-step explanation:

(A) Volume of prism = Length × width × height

                            =  11.7 × 5.4 × 9.4 = 593.9 cm³

Option B is the answer.

(B) Volume of cylinder = πr²h

                                     = π × (5)² × 10 = 250π in³

Option D is the answer.

(C) Volume of the square pyramid = $a^{2}\frac{h}{3}$

                                                          = $12^{2}(\frac{11}{3})$

                                                          = 528 cm³

Option C is the answer.

(D)  Slant height of the pyramid = 29 ft

      Height of the pyramid = $\sqrt{\text{slant height}^{2}-(\frac{\text{Length of base}}{2})^{2}}$

                                            = $\sqrt{29^{2}-21^{2} }$

                                            = $\sqrt{841-441}$

                                            = 20 ft

Now volume of the pyramid = $(\frac{1}{3})(42)^{2}(20)$

                                              = 11760 ft³

Option A. is the answer.

(E). Volume of sphere = $\frac{(A^{\frac{3}{2} } )}{6\sqrt{\pi } }$

                      3000π =  $\frac{(A^{\frac{3}{2} } )}{6\sqrt{\pi } }$

                   (3000π)² = $\frac{A^{3} }{36\pi }$

          (3000π)²(36π) = A³

                             A³ = 324×(10²)³×(π)³

                              A = (∛324)×100π

                                 = 688×π = 2158 m²

Option C. is the answer.

(F). Yes. Both the figures are similar because their corresponding sides are in the same ratio.

$\frac{3}{24}=\frac{4}{32}=\frac{14}{112}=\frac{1}{8}$

Option C. 1 : 8 is the answer.