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Questions and Answers
Solve for $a$ in $3^{2a+3}=2187$.
Solve for $a$ in $3^{2a+3}=2187$.
$a = 2$
Given that the volumes of two similar solid cones are 108 cm³ and 1715 cm³, find the ratio of their volumes.
Given that the volumes of two similar solid cones are 108 cm³ and 1715 cm³, find the ratio of their volumes.
$rac{108}{1715}$ or approximately $0.063$
What is the formula for the volume of a cone?
What is the formula for the volume of a cone?
$V = \frac{1}{3} \pi r^2 h$
If the surface area of the smaller cone is 840 cm², find the scale factor relating the two cones in terms of their linear dimensions.
If the surface area of the smaller cone is 840 cm², find the scale factor relating the two cones in terms of their linear dimensions.
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Given a surface area of 840 cm² for a smaller cone, find the curved surface area of the larger cone if the volume ratio is $\frac{108}{1715}$.
Given a surface area of 840 cm² for a smaller cone, find the curved surface area of the larger cone if the volume ratio is $\frac{108}{1715}$.
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Study Notes
Exponents and Logarithms
- The equation $3^{2a+3}=2187$ can be solved for $a$ by using exponent rules and logarithms.
Similar Solids
- If two solid cones are similar, their volumes are proportional to the cube of their corresponding linear dimensions.
- In similar solids, the ratio of the volumes is equal to the ratio of the cubes of their corresponding dimensions.
- The surface areas of similar solids are proportional to the square of their corresponding linear dimensions.
Problem Solving Strategy
- To find the curved surface area of the larger cone, use the ratio of volumes to set up a proportion, and then use the given surface area of the smaller cone to find the desired area.
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Description
Test your math skills with these problems! Solve for a in an exponential equation, and find the curved surface area of a similar solid cone.
