Class IX mensuration practice sheet..

(1) A sphere is expanded to a bigger sphere such that its volume increases by a factor of 27, find the change in its surface area.
(2) Find the volume of the biggest cone that can fit inside a cube of side 6 cm.
(3) A sphere and a right circular cylinder have the same radius. If the volume of the sphere is four times of
the volume of the cylinder, what is the ratio of the height of the cylinder to its radius?
(4) Find the surface area of the biggest sphere which can fit inside a cube of side 4a.
(5) If a hemisphere and cylinder stands on equal bases, and have the same height. Find the ratio of their
volumes.
(6) If the radius of a hemisphere is 3r, find its curved surface area.
(7) If volume of a cube is 64 cm
 3
, find its surface area.
(8) If the radius of two spheres are in the ratio 1:3, find the ratio of their volumes.
(9) If radius of a hemisphere is 2r, find its volume.
(10) If radius of a sphere is 3r, find its surface area.
(11) The area of a trapezium is 132 cm2 and the distance between its parallel sides is 6 cm. If one of the
parallel sides is of length 21 cm, find the length of the other side.
(12) A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 20 cm 3
, find the
volume of the cylinder.
(13) A sphere is perfectly enclosed inside a cube of volume 60 cm 3
. Find the volume of the sphere.
(14) The radius of a cylinder is halved and the height is doubled. What is the area of the curved surface
when compared to the same area previously?
(15) If the radii of two spheres are in ratio 5:1, find the ratio of their surface area.