Cube and Cuboid and Its Surface Areas

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

1. $h(l+b)$
2. $2(lb+bh+hl)$
3. $2h(l+b)$
4. $2(l^2+b^2+h^2)$

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.

1. $7m$
2. $\sqrt{3}m$
3. $(7-7\sqrt{3})m$
4. $(7+7\sqrt{3})m$

Q.

A tower is 100$\sqrt{3}$ m tall. Find the angle of elevation of its top from a point 100 m away from its foot.

1. ${60}^{\circ }$

2. ${45}^{\circ }$

3. ${30}^{\circ }$

4. ${15}^{\circ }$

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 .

1. 6 cm
2. 12 cm
3. 27 cm
4. 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 ${30}^{\circ }$ and ${45}^{\circ }$. 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 ____

1. $176+22\sqrt{58}{\text{m}}^2$
2. $176+\sqrt{58}{\text{m}}^2$
3. $88+22\sqrt{58}{\text{m}}^2$
4. $88+\sqrt{58}{\text{m}}^2$

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 ${60}^{\circ }$ and the angle of depression of its foot is ${45}^{\circ }$. 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 $\Delta$ 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 ${30}^{\circ }$ and the angle of elevation of the top of the tower from the foot of the building is ${60}^{\circ }$. 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.

1. True

2. 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 __ integers.

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 ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. 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 ${30}^{\circ }$. If the observer moves 20m towards the tower, the angle of elevation of the top increases by ${15}^{\circ }$. Find the height of the tower.

Q. The lateral surface area of a cube is 256 m². The volume of the cube is ______.

1. 512

Q.

A container in shape of a cylinder can store 7 litres of water. If the curved surface area of the cylinder is $1000c{m}^2$. What is the height of the cylinder?

1. 11.363 cm

2. 13.464 cm

3. 14.266 cm

4. 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 ${30}^{\circ }$, 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 ${60}^{\circ }$. 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.

1. 4
2. 5
3. 2
4. 3

Q. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is ${60}^{\circ }$ and the angle of depression of its foot is ${45}^{\circ }$. 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 ${60}^{\circ }$ and the angle of elevation of the top of the second tower from the foot of the first tower is ${30}^{\circ }$. Find the distance between the two towers and also the height of the tower.

Q.

Find the total surface area in $m^2$ 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 ${30}^{\circ }$ and the angle of elevation of the top of the tower from the foot of the building is ${60}^{\circ }$. 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 $\times$ b $\times$ h is:

1. 2(lb + bh + hl)

2. lb + bh + hl

3. 2(lh + bh)

4. lh + bh

Q. Question 11
The angle of elevation of the top of a tower is ${30}^{\circ }$. If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.