Question Text
Question 1 :
State true or false. An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in $cm^3$) is $(\frac{1}{6})\pi r^3$.
Question 2 :
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the volume of the cone (taking $\pi=\frac{22}{7}$).
Question 3 :
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?Assume $\pi$ =$\frac{22}{7}$.
Question 4 :
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 $cm^3$ of wood has a mass of 0.6 g.
Question 5 :
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost of plastering this curved surface at the rate of Rs 40 per $m^2$.Assume $\pi$ =$\frac{22}{7}$
Question 6 :
Find the volume of the right circular cone with radius 3.5 cm, height 12 cm.
Question 7 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood .
Question 8 :
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
Question 9 :
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 4989.60. If the cost of white-washing is Rs 20 per square metre, find the volume of the air inside the dome.
Question 10 :
State true or false: If the edge of the cube is a, then Diagonal of cube = $a\sqrt3$
