Question 38601This question is from textbook
: Two spheres have a radii in the ratio of 3:4. What is the ratio of their areas?
Two similar pyramids have base edges in the ratio of 3:4. What is the ratio of their volumes?
Two similar cones have a surface areas in the ratio of 16 to 25. What is the ratio of their volumes?
The measure of the angles of a triangle are in the ratio of 2: 4: 14. What is the measure of the largest angle of the triangle?
This question is from textbook
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Two spheres have a radii in the ratio of 3:4. What is the ratio of their areas?
A=4PI*R^2
HENCE AREA WILL BE IN RATIO OF SQUARE OF RADII=(3/4)^2=9/16
Two similar pyramids have base edges in the ratio of 3:4. What is the ratio of their volumes?
VOLUME OF PYRAMID =PI*BASE AREA*H/3...SO IT IS PROPORTIONAL TO BASE AREA AND H
WHEN PYRAMIDS ARE SIMILAR,EACH EDGE AND HEIGHT WILL BE IN PROPORTION.HENCE
RATIO OF VOLUMES = (3/4)(3/4)(3/4)=27/64
Two similar cones have a surface areas in the ratio of 16 to 25. What is the ratio of their volumes?
CONE AREA IS PROPORTIONAL TO PRODUCT OF RADIUS AND HEIGHT.
IN SIMILAR PYRAMIDS RADIUS AND HEIGHT WILL BE IN PROPORTION
HENCE IF AREAS OR IN 16/25 RATIO RADIUS/HT WILL BE IN RATIO OF SQRT(16/25)=4/5
VOLUME IS PROPORTIONAL TO SQUARE OF RADIUS AND HEIGHT.
HENCE RATIO OF VOLUMES =(4/5)^2*(4/5)=64/125
The measure of the angles of a triangle are in the ratio of 2: 4: 14. What is the measure of the largest angle of the triangle?
LET THE ANGLES BE 2X,4X,14X
THEIR SUM =2X+4X+14X=20X=180
X=180/20=9
SO BIGGEST ANGLE =14*9=126
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