The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:
(i) The side of the cube.
(ii) The total surface area of the cube.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
Three cubes, whose edges are x cm, 8 cm, and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
A square plate of side 'x' cm is 8 mm thick. If its volume is 2880 cm3; find the value of x.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
Each face of a cube has a perimeter equal to 32 cm. Find its surface area and its volume.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
The internal length, breadth, and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is
(i) 3 cm (ii) 4 cm (iii) 5 cm
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
When the length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm3. Find its side. How much will its volume decrease, if the length of each side of it is reduced by 20%?
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
The dimensions of a solid metallic cuboid are 72 cm × 30 cm × 75 cm. It is melted and recast into identical solid metal cubes with each edge 6 cm. Find the number of cubes formed.
Also, find the cost of polishing the surfaces of all the cubes formed at the rate Rs. 150 per sq. m.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
The dimensions of a rectangular box are in the ratio 4: 2 : 3. The difference between the cost of covering it with paper at Rs. 12 per m2 and with paper at the rate of 13.50 per m2 is Rs. 1,248. Find the dimensions of the box.
[21] Solids [Surface Area and Volume of 3-d Solids]
Chapter: [21] Solids [Surface Area and Volume of 3-d Solids]
Concept: undefined >> undefined
State for any acute angle θ whether sin θ increases or decreases as θ increases
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
Solve the following equation for A, if sin 3 A = `sqrt3 /2`
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
Calculate the value of A, if (sin A - 1) (2 cos A - 1) = 0
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If 2 sin x° − 1 = 0 and x° is an acute angle; find:
- sin x°
- x°
- cos x° and tan x°.
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If 4 cos2 x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin2 x° + cos2 x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If 4 sin2 θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos2 θ + tan2 θ.
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If sin 3A = 1 and 0 < A < 90°, find sin A
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If 2 cos 2A = `sqrt3` and A is acute,
find:
(i) A
(ii) sin 3A
(iii) sin2 (75° - A) + cos2 (45° +A)
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
If sin x + cos y = 1 and x = 30°, find the value of y
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
From the given figure,
find:
(i) cos x°
(ii) x°
(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)`
(iv) Use tan xo, to find the value of y.
[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
