# Cube and Cuboid and Its Surface Areas

## Trending Questions

**Q.**The total surface area of a cuboid with length 'l', breadth 'b' and height 'h' is

- h(l+b)
- 2(lb+bh+hl)
- 2h(l+b)
- 2(l2+b2+h2)

**Q.**From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

- 7 m
- √3 m
- (7−7√3) m
- (7+7√3) m

**Q.**

A tower is 100√3 m tall. Find the angle of elevation of its top from a point 100 m away from its foot.

60∘

45∘

30∘

15∘

**Q.**A line segment AB is divided at point C in a ratio of 5: 8 then Options: 8AC = 5AB 5AC = 8BC 8BC = 5AB 13AC = 5AB

**Q.**

**Question 5**

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot as shown in the figure. The students are to sow the seeds of flowering plants on the remaining area of the plot.

(a) Taking A as origin, find the coordinates of the vertices of the triangle.

(b) What will be the coordinates of the vertices of triangle PQR if C is the origin.

(c) Also calculate the areas of the triangles in these cases. What do you observe?

**Q.**Radius of a sphere formed by the combination of three spheres of radius 3 cm, 4 cm and 5 cm, is

- 6 cm
- 12 cm
- 27 cm
- 64 cm

**Q.**

**Question 13**

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

**Q.**A hut has cylindrical base with radius 7 m and conical top of height 3 m. The total height of the hut is 7 m. Then the Curved surface area of the hut is ____

- 176+22√58 m2
- 176+√58 m2
- 88+22√58 m2
- 88+√58 m2

**Q.**In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the

(i) quadrant OACB

(ii) shaded region.

**Q.**

**Question 12**

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.

**Q.**

**Question 5**

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for Δ ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).

**Q.**

**Question 9**

The angle of elevation of the top of a building from the foot of the tower is 30∘ and the angle of elevation of the top of the tower from the foot of the building is 60∘. If the tower is 50 m high, find the height of the building.

**Q.**

**Question 2**

Find the relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

**Q.**

**Question 2 (ii)**

Find the value of 'k', for which the following points are collinear.

(ii) (8, 1), (k, -4), (2, -5)

**Q.**

**Question 20**

If the points A(1, 2), B(0, 0) and C(a, b) are collinear, then

(A) a = b

(B) a = 2b

(C) 2a = b

(D) a = –b

**Q.**

The line segment AB can be divided in a ratio only if the given ratio is less than 1.

True

False

**Q.**

**Question 2 (i)**

Find the value of 'k', for which the following points are collinear.

(i) (7, -2), (5, 1), (3, k)

**Q.**

A line segment AB, we want to divide it in the ratio m : n, where both m and n

**Q.**A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60∘. After some time, the angle of elevation reduces to 30∘. Find the distance traveled by the balloon during the interval.

[4 MARKS]

**Q.**

**Question 3**

The angle of elevation of the top of a tower from a certain point is 30∘. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15∘. Find the height of the tower.

**Q.**The lateral surface area of a cube is 256 m

^{2}. The volume of the cube is ______.

- 512

**Q.**

A container in shape of a cylinder can store 7 litres of water. If the curved surface area of the cylinder is 1000 cm2. What is the height of the cylinder?

11.363 cm

13.464 cm

14.266 cm

22. 336 cm

**Q.**A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30∘, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60∘. Find the time taken by the car to reach the foot of the tower from this point.

**Q.**Find the value of m if the points A(5, 2), B(0, -3) and C(8, m) are collinear.

- 4
- 5
- 2
- 3

**Q.**From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.

**Q.**

**Question 13**

The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is 60∘ and the angle of elevation of the top of the second tower from the foot of the first tower is 30∘. Find the distance between the two towers and also the height of the tower.

**Q.**

Find the total surface area in m2 of a cuboid with dimensions of 26m, 14m and 6.5m respectively.

**Q.**The angle of elevation of the top of a building from the foot of the tower is 30∘ and the angle of elevation of the top of the tower from the foot of the building is 60∘. If the tower is 50 m high, find the height of the building.

**Q.**

The surface area of a box which is in the form of a cuboid whose dimensions are l × b × h is:

2(lb + bh + hl)

lb + bh + hl

2(lh + bh)

lh + bh

**Q.**

**Question 11**

The angle of elevation of the top of a tower is 30∘. If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.