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 = [tex]a^{2}\frac{h}{3}[/tex]
= [tex]12^{2}(\frac{11}{3})[/tex]
= 528 cm³
Option C is the answer.
(D) Slant height of the pyramid = 29 ft
Height of the pyramid = [tex]\sqrt{\text{slant height}^{2}-(\frac{\text{Length of base}}{2})^{2}}[/tex]
= [tex]\sqrt{29^{2}-21^{2} }[/tex]
= [tex]\sqrt{841-441}[/tex]
= 20 ft
Now volume of the pyramid = [tex](\frac{1}{3})(42)^{2}(20)[/tex]
= 11760 ft³
Option A. is the answer.
(E). Volume of sphere = [tex]\frac{(A^{\frac{3}{2} } )}{6\sqrt{\pi } }[/tex]
3000π = [tex]\frac{(A^{\frac{3}{2} } )}{6\sqrt{\pi } }[/tex]
(3000π)² = [tex]\frac{A^{3} }{36\pi }[/tex]
(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.
[tex]\frac{3}{24}=\frac{4}{32}=\frac{14}{112}=\frac{1}{8}[/tex]
Option C. 1 : 8 is the answer.
