Volume Surface Area Sainik School Entrance Exam
Class VIII Maths Sainik School Math VIII 
Posted by Priya on 2024-09-04 11:25:22 |
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Very
Short Answer Questions (Solve)
1. The total surface area of a cube
is 726 cm2. Find the length of its edge.
2. A cone has a height of 12 cm and a
base radius of 3.5 cm, how much ice cream can be put into the cone?
3. Calculate what will be the edge of the
cube if its volume is 1331 cm3.
4. Find the radius of the right circular
cylinder whose volume is 392π cm and height 8 cm?
5. Calculate what will be the surface
area of a cube whose volume is given as 216 cm3.
6. The surface area of a cube of side 27
cm is ________.
7. A right circular cylinder base area is
176 sq.cm and it has a radius of 4cm then find the height of the cylinder?
8. A heap of wheat is cone-shaped, whose
diameter is 10.5 m and height is 3 m. Find its volume. If 1m3 wheat cost
is Rs. 10, then find the total cost.
9. A cylindrical pipe has a length of
0.14 m and an internal radius is 0.09 m. Find the thickness of the pipe if its
volume is 748.
10. A right-angled triangle ABC with sides
of 3 cm, 4 cm, and 5 cm is revolved around the fixed side of 4 cm. find the
shape of the solid generated along with the total surface area of the same?
11. Calculate the surface area of a
hemispherical dome of a temple with a radius of 14 m to be whitewashed from the
outside.
12. A conical vessel has a height of 8cm
and a slant height of 10cm to find the volume of the vessel.
13. A cylinder is formed with the help of
a rectangular piece of paper find the volume of the cylinder to form?
14. If the numerical value of the volume
is equal to the numerical value of the curved surface area, and the height of
the cylinder is 5cm find the diameter of the cylinder.
15. Calculate at what speed should water
flow into it an aperture of 60 cm × 45 cm so that the level of water is raised
by 20 cm in 2.5 hours if the rectangular tank has base dimensions of 225 m ×
162 m.
16. Each edge of a cube is increased by
50%. Calculate what will be the percentage increase in the surface area of the
cube.
17. A triangle ABC which is right-angled
with dimensions of sides 5 cm, 12 cm and 13 cm is revolved around the side 5
cm. Calculate the volume of the solid so obtained. now it is revolved about the
side 12 cm, then what would be the ratio of the volumes of the two solids
obtained in two cases
18. A metallic circular cylinder is 15 cm
in height and the diameter of the base is 14 cm. It is melted and recast into
another cylinder with a radius of 14 cm. Find the height and curved surface
area of the new cylinder formed after the recasting.
19. A room’s has length, breadth, and
height are 5m, 4m, and 3m respectively. Find the cost of whitewashing the walls
of the room and the ceiling at the rate of 7.50 per m2.
20. A semi-circular sheet of metal is of a
radius of 14 cm is bent to form an open conical cup, what would be the capacity
of the same?
21. Naresh, a juice seller has set up his
juice shop. He has three types of glasses (see figure) with an inner diameter
of 5 cm to serve the customers. The height of the glasses is 10 cm. He
decided to serve the customer in ‘A’ type of glasses. (Take π = 3.14)
(i)
Find
the volume of each type of glass.
(ii) Which glass has the minimum capacity?
(iii) Which mathematical concept has been implemented in the above problem?
(iv) By choosing a glass of type A, which value is depicted by juice seller
Naresh?
22. During one of the holiday seasons,
four friends Rahul, Arun, Ajay, and Vijay went for a picnic at a hill station.
However, because of the peak season, they did not get a proper Hotel in the
city. They finally decided to make a conical tent at a park as the weather was
quite nice. They had a 200 sq. m cloth with them with which they made the
conical tent with a height of 8m and a diameter of 12m. The remaining cloth
that was left was used for the floor.
A.
Find
the slant height of the tent.
B.
How
much cloth was used?
C.
Find
the volume of the tent
D.
Find
the area of the tent
23. Shreya provides water to a village,
with a population of 4000, requiring 150 liters of water per head per day. She
has a storage tank measuring 20 m × 15 m × 6 m. For how many days will the
water in his tank last? She decreased the rate for providing water as the
dependence of villagers increased on him. Which value is depicted by her?
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