Question 1 :
State true or false: If the edge of the cube is a, then Diagonal of cube = $a\sqrt3$

Question 2 :
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions $4m\times3m$?

Question 3 :
Find the volume of a sphere whose radius is 0.63 m.

Question 4 :
Find the volume of a sphere whose radius is 7 cm.

Question 5 :
Find the amount of water displaced by a solid spherical ball of diameter 28 cm.

Question 6 :
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs12 per $m^2$ , what will be the cost of painting all these cones? (Use $\pi$ = 3.14 and take $\sqrt{1.04}$ = 1.02)

Question 7 :
30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find volume of the cylinder so formed.

Question 8 :
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Question 9 :
State true or false: Cylinder whose radius = r, height = h, it's total surface area should be $2\pi rh$.

Question 10 :
State true or false: If the radius of a cylinder is doubled and its curved surface area is not changed, then height must be halved.

Question 11 :
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

Question 12 :
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Question 13 :
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 14 :
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Question 15 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the cost of the canvas required to make the tent, if the cost of 1 $m^2$ canvas is Rs 70.

Question 16 :
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube?

Question 17 :
Find the surface area of a sphere of diameter 21 cm.

Question 18 :
State true or false: If the edge of the cube is a, then Total surface area of cube = $6a^{2}$

Question 19 :
A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required?

Question 20 :
Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.