Download App

Surface Areas and Volumes — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Areas and Volumes1 Mark
Question
The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ equals to the volume of a hemisphere of radius $r.$
✓

Answer

The height of the largest cone is $2r$ that can be fitted in a cube whose edge is $2r.$
Its volume $=\frac{1}{3}\pi\text{r}^2(2\text{r})=\frac{2}{3}\pi\text{r}^3$
But $\frac{2}{3}\pi\text{r}^3$ is the volume of a hemisphere of radius r.
Hence, the given statement is true.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from Surface Areas and Volumes→Surface Areas and Volumes — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Which of the following statements are true $(T)$ and which are false $(F)?$ In a parallelogram, the diagonals bisect each other.
→
Every rational number is a whole number.
→
Write True or False and justify your answer in the following: The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
→
Write whether the following statement are True or False.
A polynomial cannot have more than one zero.
→
The following statements are true and which are false?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
→
The following statements are true $(T)$ and which are false $(F):$ If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
→
Write True or False and justify your answer in the following: Through three collinear points a circle can be drawn.
→
A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
→
Two chords $AB$ and $CD$ of a circle are each at distances 4cm from the centre. Then $AB = CD.$
→
The following statements are true and which are false$?$ Sum of the three sides of a triangle is less than the sum of its three altitudes.
→