The cost of painting a cubical box of side 3m at the rate of Rs.2 per sq.m is
Given: Side of the cube (a) = 3 m
∴ Surface Area of Cube = 6a2 = 6 x 3 x 3 = 54 sq. cm
Now, Cost of painting the cubical box of 1 sq. m = Rs. 2 .
∴ Cost of painting the cubical box of 54 sq. m = 54 x 2 = Rs. 108
The volume of the cuboid whose length, breadth and height is 12cm, 8cm and 6cm is
Volume of cuboid = Length x Breadth x Height
⇒ V = 12 x 8 x 6 = 576 cu. cm
The base area of the cylinder is 80 sq.cm. If its height is 5cm, then its volume is
Base area of the cylinder = 80s.q cm
Now, Volume of the cylinder =
A cubical block of side 7 cm is surmounted by a hemisphere. The greatest diameter of the hemisphere is
It is clear that Maximum diameter of hemisphere can be the side of the cube.
∴ Greatest diameter of the hemisphere = 7 cm
The plural form of ‘frustum’ is
The plural form of ‘frustum’ is frusta.
A solid cylinder of radius ‘r’ and height ‘h’ is placed over other cylinder of same height and radius. The total surface area of the shape so formed is
TSA of new shape = 2πrh + 2πrh+ πr2
= 4πrh + 2πr2
The edge of the cube whose volume is 1728cm is
Given : Volume of cube = 1728 cm
The radius and height of a right circular cone and that of a right circular cylinder are respectively equal. If the volume of the cylinder is 300 cu.cm, then the volume of the cone is
Let Radius and height of the cone be r and h respectively and Radius and height of the right circular cylinder be R and H.
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. The volume of the solid is
Radii of cone and hemisphere = r = 3 cm
Height of cone (h) = 1 cm
Volume of solid = Volume of cone + Volume of hemisphere
The length of the diagonal of a cuboid of dimensions 5cm by 4cm by 3cm is
Length of the diagonal of cuboid
If two solid hemispheres of same base radius ‘x’ cm are joined together along their bases, then the CSA of the new solid formed is
If two solid hemispheres of same base radius ‘x’ cm are joined together along their bases, then the CSA of the new solid formed is 4πr2 = 4πx2.
The volumes of two spheres are in the ratio 125 : 64. The ratio of their surface areas is
Let r1 and r2 be the radius of the two spheres respectively. Therefore, the ratio of their surface areas,
If the surface area of a sphere is 36π sq. cm, then its volume is
Given: Surface area of sphere = 36πr sq. cm
∴ Volume of sphere =
A frustum of a cone is of height 12cm with radii of its circular ends as 2cm and 4cm. The volume of the frustum is
The longest rod that can be placed inside the cube is
The longest rod that can be placed inside the cube is √3 times the edge of the cube, i.e., √3 edge
If the surface area of the sphere is same as the CSA of a right circular cylinder whose height and diameter are 12cm each, then the radius of the sphere is
Let the radius of solid sphere be rr cm and radius of solid cylinder be R cm. Then according to question,
If the volume of a cube is 343 cm , then its edge is
The inner dimensions of a closed box are 12cm, 10cm and 8cm. If the thickness of the wood is 1cm, then the capacity f the box is
Given: l = 12 cm, b = 10 cm and h = 8 cm
∴ Capacity of a closed box = lbh = 12 x 10 x 8 = 960 cm. cm
Capacity of box of thickness 1 cm = 960/1 = 960 cu. cm
A funnel is the combination of
A funnel is the combination of a frustum of a cone and a cylinder.
A plumbline is combination of
A plumbline is combination of a hemisphere and a cone
A rectangular piece of paper is 44cm long and 18cm wide. If a cylinder is formed by rolling the paper along its length, then the radius of the base of the cylinder is
Let r be the radius of the cylinder. Given: Circumference of cylinder = 44 cm
The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is
Let r1 and r2 be the radius of the two spheres respectively. Therefore. the ratio of their volumes.
Now, ratio of thier volumes,
During conversion of a solid from one shape to another, the volume of the new shape will
During conversion of a solid from one shape to another, the volume of the new shape will remain unaltered.
The shape of a glass tumbler is usually in the form of
The shape of a glass tumbler is usually in the form of frustum of a cone.
A cylindrical pencil sharpened at one edge is the combination of
A cylindrical pencil sharpened at one edge is the combination of a cone and a cylinder.