Question 1 :
State true or false: A triangle is unique if three sides are given.

Question 2 :
State true/false, a triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 cm.

Question 3 :
State true or false: A triangle is unique if two sides and the included angle is given.

Question 4 :
State true/false, a triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.

Question 5 :
The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to

Question 6 :
State true or false: An angle of 67.5° can be constructed.

Question 9 :
_____________ construction means using only a ruler and a pair of compasses as geometrical instruments.

Question 10 :
With the help of a ruler and a compass it is not possible to construct an angle of

Question 11 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Total surface area of cuboid = 2 ( lb + bh + hl )

Question 12 :
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per $m^2$ .

Question 13 :
If the volume of a right circular cone of height 9 cm is 48 $\pi$ $cm^3$ , find the diameter of its base.

Question 14 :
A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

Question 15 :
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recasted into a sphere. Find the radius of the sphere.

Question 16 :
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Question 17 :
The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

Question 18 :
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Question 19 :
Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Question 20 :
A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Question 21 :
A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume of the solid so formed.

Question 22 :
State true or false: Sphere whose radius = r, the surface area must be $4\pi r^{2}$.

Question 23 :
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find its inner curved surface area.Assume $\pi$ =$\frac{22}{7}$.

Question 24 :
Find the volume of a sphere whose radius is 0.63 m.

Question 26 :
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 27 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d238f59b460d7261f569.jpeg' /> In the above image, a child playing with building blocks, which are of the shape of cubes, has built a structure as shown. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Question 28 :
State true or false: Curved surface area of hemisphere is $2\pi r^{2}$.

Question 29 :
The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Question 30 :
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.Assume $\pi$ =$\frac{22}{7}$.

Question 31 :
A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m. For how many days will the water of this tank last?

Question 32 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d240f59b460d7261f575.jpeg' /> In the above image, a wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per $cm^2$ and the rate of painting is 10 paise per $cm^2$ , find the total expenses required for polishing and painting the surface of the bookshelf.

Question 33 :
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 34 :
A solid cube of side 12 cm is cut into eight cubes of equal volume.Find the ratio between their surface areas.

Question 35 :
Find the total surface area of a cone whose radius is $\frac{r}{2}$ and slant height 2l.

Question 36 :
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Question 37 :
State true or false: 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.

Question 38 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d237f59b460d7261f568.jpeg' /> In the above image, a hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs 5 per 100 $cm^2$

Question 39 :
The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. Find the ratio of their volumes.

Question 40 :
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?