Podcast Beta
Questions and Answers
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.
$rac{108}{1715}$ or approximately $0.063$
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.
Signup and view all the answers
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 $\frac{108}{1715}$.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
