Curved Surface Area & Total Surface Area of a Pyramid

Q.

The output of the given combination gates represents :

1. XOR Gate

2. NOR Gate

3. NAND Gate

4. AND Gate

Q.

Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.

1. $120m^2$

2. $140m^2$

3. $240m^2$

4. $340m^2$

Q.

A tent in the form of a square pyramid has a height of 12 cm and the base edge length is 18 cm. Find the total cloth required to build the tent.

1. $324c{m}^2$

2. $834c{m}^2$

3. $510c{m}^2$

4. $540c{m}^2$

Q.

The angle opposite to the base edge of a square pyramid on its lateral face is 60${}^{\circ }$. If the slant height of the pyramid is 40$cm$, what is the lateral surface area of the pyramid?

1. $\frac{3200}{\sqrt{3}}cm$​​​

2. $\frac{800}{\sqrt{3}}cm$​​​

3. $\frac{400}{\sqrt{3}}cm$​​​

4. $\frac{6400}{\sqrt{3}}cm$​​​

Q.

The base edge of a square pyramid with slant height 24cm is 14cm. Then its lateral edge is:

1. 22 cm

2. 32 cm

3. 25 cm

4. 30 cm

Q.

What is the surface area of a square pyramid with a base side length of $9cm$ and a slant height of $7cm$?

Q.

All edges of a square pyramid are of equal lengths. If the length of the base edge is $20cm$, what is the lateral surface area?

1. $400\sqrt{3}$

2. $100\sqrt{3}$

3. $300\sqrt{3}$

4. $200\sqrt{3}$

Q. Find the lateral surface area, total surface area and volume of a square pyramid with the following specification: a = base edge length, h = slant height and H = height.

Q.

The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the lateral edge is $50cm$. What is its lateral surface area?

1. $2500\sqrt{3}$

2. $2500(1+\sqrt{3})$

3. $2500(2+\sqrt{3})$

4. 2500

Q. What is the total surface area of the square pyramid whose base edge is 6 cm long and the lateral faces are equilateral triangles?

Q.

Which of the following represent(s) the total Surface area of a square pyramid?

1. Base area + Lateral Surface area

2. ${\text{(Base Edge)}}^2+\frac{1}{2}\times \text{base edge}\times \text{slant height}$

3. $\frac{1}{2}\times \text{base edge}\times \text{slant height}$

4. ${\text{(Base Edge)}}^2+4\times (\frac{1}{2}\times \text{base edge}\times \text{slant height})$

Q. If a piece of cloth costs $₹10/m^2,$ then find the total cost to build a square pyramid tent of base edge 10 m and slant height 10 m.

Q. Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.

Q. A square pyramid covers an area of $400m^2$ on the ground.
If the height of the pyramid is 10 m, then find the total surface area of the pyramid.

Q.

All edges of a square pyramid are of equal lengths. If the length of the base edge is $20cm$, what is the total surface area?

1. $400\sqrt{3}$

2. $400(1+\sqrt{3})$

3. $100(1+\sqrt{3})$

4. $400(3+\sqrt{3})$

Q.

The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the base edge is $50cm$. What is its surface area?

1. 2500

2. $2500(1+\sqrt{3})$

3. $2500\sqrt{3}$

4. $2500(2+\sqrt{3})$

Q.

The angle opposite to the base edge of a square pyramid on its lateral face is 30${}^{\circ }$. If the slant height of the pyramid is 20$cm$, what is the lateral surface area of the pyramid? (Note that $tan{15}^{\circ }=0.268$)

1. $4288c{m}^2$​​​

2. $428.8c{m}^2$​​​

3. $42.88c{m}^2$​​​

4. $600c{m}^2$​​​

Q. If a piece of cloth costs $₹10/m^2,$ then the total cost to build a square pyramid tent of base edge 10 m and slant height 10 m is .

1. ₹ 1000
2. ₹ 2000
3. ₹ 3000
4. ₹ 4000

Q. Find the perimeter of a triangular-based pyramid with slant height $18$m and lateral surface area $360m^2$.

Q. Find the difference between the lateral and total surface area of a square-based pyramid with side $2.5$cm and slant height $8$cm.

1. $6.25cm$
2. $6.68cm$
3. $6.75cm$
4. $6.93cm$

Q.

What is the total surface area of the square pyramid whose base edge is 6 cm long and the lateral faces are equilateral triangles?

1. $9\sqrt{3}c{m}^2$

2. $36(1+\sqrt{3})c{m}^2$

3. $36c{m}^2$

4. $56c{m}^2$

Q. Find the lateral and total surface area of the following pyramids.
(a) Square-based pyramid with base $6$cm and slant height $14$cm;
(b) Triangular-based pyramid with base $12$cm and slant height $20$cm.

Q. A square pyramid covers an area of $400m^2$ on the ground.
If the height of the pyramid is 10 m, then the total surface area of the pyramid is .

1. $985.68m^2$
2. $975.68m^2$
3. $965.68m^2$

Q. $\text{Match the following for a square pyramid.}$ Where, a = base edge length, h = slant height and H = height

1. $2ah$
2. $a^2+2ah$
3. $\frac{1}{3}{a}^{2}H$

Q. The base and height of a square-based pyramid is $10$cm and $12$cm respectively. Find its total surface area.

Q. Find the area of a triangle in cm${}^2$; whose sides are: $21cm,28cm$ and $35cm$.

Q. Find the slant height of a square based right pyramid whose perimeter of the base is $40$m and its lateral surface area is $120m^2$. What is its total surface area?

Q.

Find the total surface area of a pyramid given the base edge is 14 cm and the lateral edge is 9 cm.

1. $14(7+4\sqrt{2})c{m}^2$

2. $28(7+4\sqrt{2})c{m}^2$

3. $4\sqrt{2}c{m}^2$

4. $84c{m}^2$

Q. Find the surface area(in $c{m}^2$) of the square pyramid shown below

Q. In a convex polygon of $6$ sides two diagonals are selected at random. The probability that they intersect at an interior point of the polygon is:

1. $\frac{2}{5}$
2. $\frac{5}{12}$
3. $\frac{7}{12}$
4. $\frac{3}{5}$